First, a point I forgot to address:
There is no need to decide on a transcription. He already did that himself.
That is not exactly relevant because, as I mentioned, the transcription standards back in those days were different. Today nobody transcribes -ов as -off. And since language evolves, it would only be natural that current usage would reflect today's standards and not those of the 1940s.
and if you want that to be your name, you can legally change it to that (I guess, I don't know how that works in Poland).
Irrelevant again - that is a legal matter, it has little to do with what we are discussing. For example, many people decide to publish under a nome de plume (which is not their "legal" name), and in effect come down to posterity under their pseudonym - often contrary to what they would have wished!
when you have your work published, you are entitled to have your name on the publication in the form you chose.
Until your work ends up in a library - where it is the librarian who decides under which heading to put it in the catalog...
But I digress.
After all, I thought we were supposed ot be in the company of at least somewhat educated people here
Not only is that irrelevant - it is also not true. The forum is open to anybody interested in music, no matter what their education. Similarly, language is the way the majority speak, not just some sort of educated sub-group.
Note that my reasoning alone does not imply that either of the spellings is "more correct" - to establish that you need to know which spelling the majority of English-speakers use. It seems quite likely that they in fact use the spelling you prefer, at least Americans do. In the BYU Corpus of American English the number of tokens for "Rachmaninov" is far, far greater than for "Rachmaninoff".
OTOH, if you go to amazon.com and do a search for "Rachmaninoff" and "Rachmaninov", you will find that the latter constitutes 80% of the total number of results in the "Music" category. Since the way CDs are labeled is decided by educated folk rather than the masses, it would seem that only under your line of reasoning is "Rachmaninov" the spelling everyone should adhere to.
Not to spoil the fun, but, unless we're talking about the inflection of a name qua noun of a given declension (and that really only goes for highly inflected languages, by which I mean, languages more inflected than English), systematic grammar and syntax - the summa of any sophisticated language - are rarely concerned with names. (This goes at least for the Romance/Germanic families, and I can't speak for other IE language groups.) So, as far as language is concerned, names aren't any more or less important than any other noun in a given declension.
Now, that point is entirely moot in English, since much of the case indication (except in pronouns, and, even then, there isn't a whole lot of inflection) is done with prepositions. Since names aren't the concern of formal language, we're left with social convention. In that case, it's terrible form to tell someone that their spelling or pronunciation is incorrect. They get to determine those things for themselves.
Don't see your point here at all. What has inflection got to do with anything? The way certain words are classified as proper nouns has absolutely nothing
to do with inflection. In fact, the only formal criterion I can think of is the capitalization of proper names. Grammatically, whether you're talking about inflected languages or not, proper names are no different
than any other word, or any other noun, to be exact.