Who were the Minim (מינים), and who were the Moaminim (מאמינים) ?
Wikipedia records, in two articles I have provided quotes from and links to, that the first believers in Yeshua were called “Minim” by their detractors:
Hilchot Teshuva Chapter 3 Halacha 7 
Five peoples who can be classified as Minim
One who denies the existence of God or the ruler of the world
One who says there are two or more rulers of the world
One who accept there is one Master of the world but maintains He has a body or a form
One who denies that He is the sole First Being and Creator of all existence
One who serves entities that serve as intermediary between him and the eternal Lord such as stars, constellations or any other entity
According to Hilchot Teshuva 3:6 Minim do not have a portion in the world to come. Their souls are cut off and they are judged for their sins.
The Birkat haMinim is a benediction on heretics. (…) Modern scholarship however has generally evaluated that the benediction probably did originally include Jewish Christians before Christianity became markedly a Gentile religion.
The Birkat ha-Minim, (Hebrew ברכת המינים “Blessing on the heretics”), is a Jewish prayer of blessing on heretics in general, and sometimes Christians, though in this context “blessing” may also be a euphemism for a curse.
The writing of the benediction is attributed to Shmuel ha-Katan at the supposed Council of Jamnia which was inserted in the “Eighteen Benedictions” as the 19th blessing in the silent prayer to be said thrice daily, the Amidah. The benediction is thus seen as related to the Pharisees, the Development of the Hebrew Bible canon, the split of early Christianity and Judaism as heresy in Judaism, the origins of Rabbinic Judaism, Origins of Christianity, Christianity in the 1st century, and history of early Christianity.
The blessing exists in various forms. (…) two medieval Cairo Genizah copies equate Minim and Notzrim “Nazarenes”, “Christians.”
Identification of Minim
Main article: Minuth
The extent of the minim included by the birkat is debated. During the medieval period, whether the birkat had historically included Christians or not became both a part of disputations, a pretext for persecution, and a cause for concern for the safety of Jewish communities. It is generally viewed in modern studies that the term “heretics” at an early point in the split between Christianity and Judaism had included Jewish apostates to Christianity.
(…) Many scholars have seen reference to the Birkat haMinim in Justin Martyr’s complaint to Trypho of the Jews “cursing in your synagogues those that believe on Christ.”
Before we can discover the true significance of the term “MINIM” (which is usually translated as Destroyers or Heretics) we must ask ourselves a question which most neglect to ask:
“What or which term did the first century believers in Yeshua call themselves ?”
Was it Christians ?
Was it Galileeans ?
Was it Nazarenes ?
They were certainly called these names — by others.
But what did they call themselves ?
You can do a scripture search and find the proof yourself, or you can keep reading if you want to spoil the fun of finding out yourself.
The term used most often in the scriptures to describe the first century believers is…. *drum roll* BELIEVERS. This can be verified by a simple search through any Bible search engine (for example Biblos.com)
The term “Believers” is used far more times than either Christian(s), Galileean(s), Nazarene(s) or any such titles.
Indeed, all these three titles (Christian, Galileean, Nazarene) are only ever recorded as being applied to the Believers by pagans and non-Believers.
The Believers themselves, when referring to each other, use the term Believer(s).
In Greek, this would be pronounced Piston, and in other ways derived from the root word pistis, such as Pisteuontes.
In Hebrew, it would be pronounced somewhat like Moaminim, or perhaps Maaminim (מאמינים) which is grammatically related to the word Amen and Emunah/faith.
[Note, the term “Christian” has been inserted in several translations in verses where it does not occur in any manuscripts, usually as an adjective to the term “brother”, supposedly to clarify the text.]
Of course, none of these are “official names” or brand names in the modern sense, for such conceptuality and formalism was rejected by the true Believers.
This then sheds interesting light on the curse uttered over the Believers in the synagogues; they were namely called “destroyers”, or MINIM; we can see that the first two hebrew letters (mem-aleph) have been removed to transform it from MOAMINIM to MINIM.
The term Moaminim was therefore being used so frequently to describe the Believers in Yeshua that their detractors found it natural or obvious to make a derogatory term out of their apellation, by turning “Believers” (מאמינים) into “Destroyers” (מינים).
If you don’t like the “sound” of Moaminim, if you think it sounds “too middle-eastern” or “too Muslim” even; well “tuff”.
That’s like complaining that “Nazarene” and “Nazirite” sounds like “Nazi”.
Of course, NEITHER Christian(s) nor Nazarene(s) nor Moamin(im) are or were demonstrably “official titles”, in our modern formalist sense of the word. In fact, they never had such a title.
I guess you can call yourself what you want.
However, I don’t see why anyone would imitate and repeat the technical terms and names invented by non-believers, when one could use the word used by Believers to describe themselves.
Note that while Christians call their religion “Christianity”, the Believers didn’t call their religion by a word directly tied to the name they called themselves; rather, their religion was clearly called “The Way”, assuming it even had a name in our sense of the term.
“The Way”, or in Hebrew “HADEREK” would have been the closest thing to an actual name or “-ism”, but without actually being an “-ism.”
It is clear that the Minim (“Destroyers”) were identical to the Moaminim (“Believers”); in the Scriptures they never called themselves Minim, of course, but only ever called themselves Moaminim, and also Achim (“Brethren”), neither of which are actual technical terms.
We can certainly call ourselves Galileeans/Christians/Messianics or what have you, but as for what the scriptures show the first Galileeans/Christians/Messianics called themselves, the evidence is unmistakable and unshakable, and their example not lightly ignored.
I’m not saying people or groups with labels like “Christian” or “Nazarene”, etc, in their titles, should change their titles; rather we should take these names and labels we apply to ourselves less seriously, for the scriptures clearly eschew this type of formality and on the most part avoid any technical terms; we should realize the names and labels we invent are simply identifying descriptors, and not divinely mandated appelations; the organizations we create in this modern world of formalism have to have official titles as per modern expectations and tax exemption form requirements, but the ancient congregations of the believers certainly knew nothing of such practices, for even the few terms they applied to themselves were devoid of technicality and sectarianism.
Regardless of what you want to draw from it, the scriptures speak for themselves, and the primary terms used by believers in Yeshua to describe THEMSELVES are:
Moaminim / Maaminim, and Achim; their religion is called, by them, “the Way” (which would be “Haderek” in Hebrew.)
We’re not compelled to use these terms, but by scriptural example they are as good as any.