The name Mithras (Latin, equivalent to Greek "Μίθρας") is a form of Mithra, the name of an old, pre-Zoroastrian, and, later on, Zoroastrian, god — a relationship understood by Mithraic scholars since the days of Franz Cumont. An early example of the Greek form of the name is in a 4th century BCE work by Xenophon, the Cyropaedia, which is a biography of the Persian king Cyrus the Great.

The exact form of a Latin or classical Greek word varies due to the grammatical process of declension. There is archaeological evidence that in Latin worshippers wrote the nominative form of the god's name as "Mithras". However, in Porphyry's Greek text De Abstinentia (Περὶ ἀποχῆς ἐμψύχων), there is a reference to the now-lost histories of the Mithraic mysteries by Euboulus and Pallas, the wording of which suggests that these authors treated the name "Mithra" as an indeclinable foreign word.

Related deity-names in other languages include:

Vedic Sanskrit Mitra, "friend, friendship," as the name of a god praised in the Rigveda.  In Sanskrit, mitra is a name of the sun god, mostly known as "Surya" or "Aditya".

The oldest form of the inscription 'mi-it-ra' is  found in an inscribed peace treaty between the Hittites and the kingdom of Mitanni, from about 1400 BCE.

Mitanni

An Indo-Iranian empire centred in northern Mesopotamia that flourished from about 1500 to about 1360 BC. At its height the empire extended from Kirkūk (ancient Arrapkha) and the Zagros Mountains in the east through Assyria to the Mediterranean Sea in the west. Its heartland was the Khābūr River region, where Wassukkani, its capital, was probably located.

Mitanni was one of several kingdoms and small states (another being Hurri) founded by the Indo-Iranians in Mesopotamia and Syria. Although originally these Indo-Iranians were probably members of Aryan tribes that later settled in India, they apparently broke off from the main tribes on the way and migrated to Mesopotamia instead. There they settled among the Hurrian peoples and soon became the ruling noble class, called maryannu.

https://www.britannica.com/place/Mitanni

In what is perhaps the oldest treaty between the Hittites and Mitanni (between Suppiluliuma and Shattiwaza, c. 1380 BC), the deities Mitra, Varuna, Indra, and Nasatya (Ashvins) are invoked. Kikkuli's horse training text (circa 1400 BC) includes technical terms such as aika (Vedic Sanskrit eka, one), tera (tri, three), panza (pañca, five), satta (sapta, seven), na (nava, nine), vartana (vartana, round). The numeral aika "one" is of particular importance because it places the superstrate in the vicinity of Indo-Aryan proper (Vedic Sanskrit eka, with regular contraction of /ai/ to [eː]) as opposed to Indo-Iranian or early Iranian (which has *aiva; compare Vedic eva "only") in general.

This treaty is extremely important because it points to something astonishing: the possibility that Vedic  Sanskrit did not originate in India. David Anthony in his book, 'The Horse, the Wheel, and Language' states that this shows that the Sanskrit of the Rigvedic Sanskrit actually predates the collection that makes up the Rig Veda in Northwestern India, including the “central religious pantheon and moral beliefs enshrined in the Rig Veda existed equally early”.

Iranian Mithra and Sanskrit Mitra are further believed to come from the  Indo-Aryan word mitrás, meaning "contract, agreement, covenant".

Modern historians have different conceptions about whether these names refer to the same god or not. John R. Hinnells has written of Mitra/Mithra/Mithras as a single deity worshipped in several different religions.  On the other hand, David Ulansey considers the bull-slaying Mithras to be a new god who began to be worshipped in the 1st century BCE, and to whom an old name was applied.

Mary Boyce, a researcher of ancient Iranian religions, writes that even though Roman Mithraism seems to have had less Iranian content than historians used to think, nonetheless "as the name Mithras alone shows, this content was of some importance".

Transcription of cuneiform                 Interpretation             Vedic equivalent

a-ru-na, ú-ru-wa-na                                  Varuna                        Varuṇa

mi-it-ra                                                        Mitra                            Mitra

in-tar, in-da-ra                                            Indra                            Indra

na-ša-ti-ya-an-na                                      Nasatya(-nna)             Nāsatya

a-ak-ni-iš                                                    Āgnis                            Agni

Much about the cult of Mithras is only known from reliefs and sculptures. There have been many attempts to interpret this material.

This is a key point worth noting.

Mithras-worship in the Roman Empire was characterized by images of the god slaughtering a bull. Other images of Mithras are found in the Roman temples, for instance Mithras banqueting with Sol, and depictions of the birth of Mithras from a rock. But the image of bull-slaying (tauroctony) is always in the central niche.  Textual sources for a reconstruction of the theology behind this iconography are very rare.

The practice of depicting the god slaying a bull seems to be specific to Roman Mithraism. According to David Ulansey, this is "perhaps the most important example" of evident difference between Iranian and Roman traditions: "... there is no evidence that the Iranian god Mithra ever had anything to do with killing a bull."

This is another key point worth noting.

https://en.wikipedia.org/wiki/Mithraism