Its synonyms are - Aag,  Anal,  Bhooritej,  Chitrabhaanu,  Havyavaahan,  Hutaashan,  Jaatavedaa,  Jwaalaa,  Paarthiv,  Paavak,  Pingesh,  Plavang,  Rudragarv,  Hiranyakrit,  Shikhee,  Vahni,  Vaishwaanar,  Vibhaavasu.

According to MBH, G-3-Youth/22, Once Sahadev (one of the Paandav) went for victory tour at the time of Yudhishthir's Raajsooya Yagya, he met a King named Neel who was protected by Agni Dev, so as he wanted to defeat him, Agni Dev restricted him. So he prayed him - "I bow you, my efforts are only for you. You are called Paavak because you sanctify everything. You are the mouth of gods and you are Havyavaahan because you carry the Ghee poured on you. You are called Jaatavedaa because Ved have emerged for ministering you. You are called Chitrabhaanu because you are the chief of Devtaa, Anal, Vibhaavasu, Hutaashan, Jwaalaa, Shikhee, Vaishwaanar, Pingesh, Plavang, Bhooritej. You are the same from whom Kumaar (Skand) has taken birth. You are called Rudragarv and Hiranyakrit...."

(1) Sacred fire. Agni is of several kinds -
(a) "Aavaahneeya" Agni - The Heavenly Agni appears as Soorya (Sun)
(b) "Dakshinaagni" Agni - The atmospheric Agni appears as lightning
(c) "Gaarhapatya" Agni - The Earthly Agni appears at worship, for cooking and digests the food inside the body of living beings.
(d) "Vaidik" Agni - this fire is kindled for Vaidik rituals. Both are different.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Aangiras (P 30) lists other types of Fire also - 
(1) Vaishwaanar Agni - belonging to all men; 
(2) Usharbudh Agni - the one who arrives in the house when the morning fire is kindled; 
(3) Havyavaahan Agni - Havya means offering to Devtaa through fire and Vaahan means carrier or ride; so Havyavaahan means one that carries the oblations of men to Devtaa; 
(4) Paavak - the one who purifies; it is a synonym of Agni also; and
(5) Jaatved - the one who knows all that is born.

Also called Vahni. The eight forms of Vahni (Fire) are
(1) Jaatved - which according to Saayan's commentary on Rig Ved, means "known by itself as it is born or spreads" or "known by those who are born"
(2) Sapt-Jivhaa - Who has seven tongues   (see Tongues of Fire below)
(3) Vaishwaanar - from Vaishwaanar (ruling or benefiting all men - a name of Saavitree)
(4) Havya-Vaahan - Which carries the oblations to gods
(5) Ashwodar-ja - Badavaanal or Badavaagni - literally Mare's Fire (fires of lower regions)
(6) Kaumaar-Tejah - The Fir or Seed from which Kumaar or Kaarttikeya was born
(7) Vishwa-Mukh - Since it can devour the Universe, it is called Vishwa-Mukh
(8) Dev-Mukh - Because as all oblations are offered to him, he is the mouth of Devtaa.

Agni has 10 Kalaa - (1) Dhoomraa, (2) Archi, (3) Ooshmaa, (4) Jwalinee, (5) Jwaalinee, (6) Vis-phulinginee, (7) Sushree, (8) Suroopaa, (9) Kapilaa, (10) Havya-Kavyavaahaa.
(Naarad Puraan, p 414)

The Agni Deity
Fire god or Agni Dev. He is very important as Vaidik Devtaa, second only to Indra. He is said to be the messenger priest who carries man's offerings to various Devtaa. He have seven tongues - (1) Hiranyaa, (2) Kanakaa, (3) Raktaa, (4) Aaraktaa, (5) Suprabhaa, (6) Bahuroopaa, and (7) Satee. Meditating upon these seven tongue-Devee gives all kinds of fruits. 
(Bhavishya Puraan, p. 254)       [See also Tongues of Fire below]

A. Mission and special features - Providing the path for dispersion of Deities from the absolute ether (Aakaash) element to the site of the fire sacrifice (Yagya). Every spiritual rite (Sanskaar) is performed in the presence of fire. In the Indian scriptures of Deities, Agni is accorded status only next to Indra, the king of Deities. In the Rig Ved, Agni is referred to as the presiding Deity of the home (Grihapati) and an excellent guest. He is the liaison between Deities and man. Since it is he who delivers the oblations offered in the Fire (Havi) by man to deities in every spiritual rite he is invoked on the altar (Sthandil) first. The name of Agni used in every spiritual rite varies. After the ritual of invoking Agni, oblations are offered to the principal deities through it and then the respective spiritual rites are performed. He is the presiding deity of the south-western direction

B. Science behind the idol - The idol has three eyes, four teeth and four arms. It sports a beard and smoky grey clothing and is red in complexion.

C. Family - Consorts - Swaahaa and Swadhaa. "Swaahaa - She is one of the consorts of Lord Agni. When performing a sacrificial fire (Hom), at the end of a Mantra an oblation is offered after chanting Swaahaa only because it is believed that a sacrificial fire bestows benefits only if Swaahaa is uttered in this way. When praying to Agni, Sage Grutsamad says, “O Agni deliver the oblation offered through the fire amidst chanting of the word Swaahaa to deities.” (Rig Ved 2.3.11).

According to MBH, G-3-Youth/22, Agni Dev married King Neel's daughter also. Her name is not given there.

D. Spiritual practice - Hindu and Zoroastrians worship Agni. Agnihotree - He is the one who performs the ritual of Agnihotra, that is concentrates on Agni and keeps a fire lit in his home throughout his life. He ritualistically worships the Gaarhapatya, Aahvaaneeya and Dakshinaagni fires everyday in the morning and evening. Some Agnihotree offer oblations to the Gaarhapatya fire in the morning and evening and to the Aahvaaneeya and Dakshinaagni Fires only during the day. The sacred fire is offered oblations twice, at sunrise in the morning and after sunset in the evening. In the morning, an oblation is offered to the Soorya Deity and in the evening to Agni. Agnihotree also give offerings to all living beings and the seven great sages (Saptarshi) along with the fire. An Agnihotree couple has to carry the fire with them even during travel. An oblation offered to it consists of sacrificial firewood (Samidhaa), milk and water.

The Tongues of Agni (Fire)
Yagya Datt Muni has told that Agni has three Jihvaa (tongue or flames) - Hiranyaa, Kanakaa, and Krishnaa; but with the difference of their types, these Jihvaa are of seven types - (1) Vishwamoorti, (2) Sphulinginee, (3) Dhoomravarnaa, (4) Manojavaa, (5) Lohitaasyaa, (6) Karaalaasyaa, (7) Kaalee.

These tongues are different with the difference of Samidhaa. Bahuroopaa, Atiroopaa, and Saatwikaa - these Agni Jihvaa are used in Yog Karm. 

In Aagyaa Hom it becomes Hiranyaa Agni; 
by doing Havan with Tri-Madhu (milk, sugar and honey mixed in equal quantity) it becomes Karnikaa Agni; 
by doing Havan with pure milk it becomes Raktaa Agni; 
in Naityik (daily) Karm it becomes Prabhaa Agni; 
in Pushp Hom it becomes Bahuroopaa Agni; 
when doing Havan with Ann and Kheer it becomes Krishnaa Agni; 
in Ikshu Hom it becomes Paraagaa Agni; 
in Padm Hom it becomes Suvarnaa and Lohitaa Agni; 
when Havan is done with Bilva leaves it becomes Shwetaa Agni; 
in Til (sesame seed) Hom it becomes Dhoominee Agni; 
in Kaashth (wood) Hom it becomes Karaalikaa Agni; 
in Pitra Hom it becomes Lohitaasyaa Agni; 
in Dev Hom it becomes Manojavaa Agni. 

Whatever Samidhaa (the wood or the material to be put in fire) is used in Havan, Vaishwaanar Dev exists in those Samidhaa. When an Aahuti is offered in Agni. Agni Dev helps in all phases of life. One should offer Aahuti in the mouth of Agni, if it is offered at some other place it gives wrong results. Hiranyaa is the tongue of Agni while offering Aahuti with Ghee; while in other Aahuti it is called Gananaa, Vakraa, Krishnaabhaa, Suprabhaa, Bahuroopaa, and Atiroopaa.
(Bhavishya Puraan, p 238)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mahaanirvaan Tantra (p 196) describes seven tongues of Fire like this -
(1) Kaalee - the Black One which brings about the end at the destined time (Maarkandeya Puraan, xcix, Hymn to Agni)
(2) Karaalee - the Dreadful One - the cause of the Great Dissolution of the world (Maarkandeya Puraan, xcix, Hymn to Agni)
(3) Manojavaa - swift as thought because of its quality of lightness (Maarkandeya Puraan, xcix, Hymn to Agni), 
(4) Sulohitaa - the Ruddy One, very red which accomplishes the desire of created things (Maarkandeya Puraan, xcix, Hymn to Agni)
(5) Su-Dhoomra Varnaa - who is of smoky color which causes sickness amongst breathings (Maarkandeya Puraan, xcix, Hymn to Agni)
(6) Sphulinginee - having sparks of Fire because it is altogether shapeless (Maarkandeya Puraan, xcix, Hymn to Agni)
(7) Vishwa-Niroopinee - that which makes manifest Universe, bestows blessings on all breathing things (Maarkandeya Puraan, xcix, Hymn to Agni). The Puraan reads Vishwaas-da (bestowing confidence), or Vishwa-srij (creating the Universe)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Seven tongues of Fire are described thus in Naarad Puraan -
(1) Hiranyaa, (2) Kanakaa, (3) Raktaa, (4) Aaraktaa, (5) Suprabhaa, (6) Bahuroopaa, and (7) Satee.
(Bhavishya Puraan, p 254)

Names of Agni in Various Tyes of Yagya
The Shat-Karm Deepikaa says that ---
in Poorn Aahuti, the Fire is called Mri-da
in Shaanti Kriyaa it is called Varad,
in Pushti Kriyaa it is called Balad
in Abhichaar it is called Krodh
in Vasheekarn it is called Kaamad
in Varadaan it is called Choodak
in Laksh Hom it is called Vahni
in Koti Hom it is called Hutaashan