I've never learned a term for this and I can't think of a direct analogy in English.
This kind of word formation is much more productive in ASL (and in sign languages generally) than in English (and spoken languages generally). I've listed the examples you gave, and a few more:
[T]rigonometry, [A]lgebra, [C]alculus, ...
[Y]ellow, [B]lue, ...
[F]amily, [G]roup, [C]lass, ...
[L]aw, [R]egulation, [E]thics, ...
 week ago,  weeks ago,  weeks ago, (etc., all the way up to nine)
 month,  months, (etc., all the way up to nine)
Is there a recognized way of referring to these groups of words?
These are frames. A frame is, in all the examples up there, the way the hand moves, plus non-manual features, but is not a complete sign (and so does not have a "complete" meaning). The sign is completed by adding a handshape. The examples in the Wikipedia link are completed by adding the handshape from another ASL word, but the examples up there are completed by adding the handshape from [the initial letter of] an English word or a numerical digit.
Though it's called "frame" in some literature about sign languages, it could also be called a transfix. These are well known from some languages of Africa and the Middle East (most famously, Arabic, Hebrew, ...) and it's a similar approach to word formation. Some examples from Arabic:
- sayyāra (a car)
- ḡassāla (a washing machine)
- ṯallāja (refrigerator)
Now, consonant + a + consonant doubled-up + vowel + consonant + a, is kind of like a template, one which roughly means "machine which ...". And you plug in three consonants: "s-y-r" means "something to do with travelling or movement", and "ḡ-s-l" means "something to do with cleaning up". "ṯ-l-j" means "something to do with snow". You can see many other words derived from these "three consonant roots", but these, and that template, are absolutely impossible to pronounce on their own.
In the same way, for
x weeks ago, the non-dominant forearm is held horizontally, and the dominant hand moves from the elbow toward the non-dominant fingertips, and then turns upward and over the shoulder. That whole thing is also kind of a template, which you plug in some more phonemic content to produce an actual word. You can see that this too is impossible to enunciate on its own, i.e. without your right hand actually having a handshape.
I've been taught that unnecessary initialization is sometimes seen as undesirable in the Deaf community. Does that still apply to words like this, where initialization is the only way of distinguishing them?
It doesn't apply here, because without the initial, you'd just be left with the "frame", which is impossible to produce in isolation!, and which would not carry enough meaning by itself anyway. The sign you know for family, really is the entire sign.