In practice, yes.

I have two middle names; most financial service providers decline to recognise my second middle-name. Same goes for the taxman and my pension provider. It seems that a "full name" is no longer a canonical identifier for a person, just really a kind of nickname; the canonical identifier is now an account-number, employee-ID or whatever.

Thanks to marriage, names were non-canonical before the computer was even invented.

And thanks to people moving house, or even changing profession, or acquiring some defining trait or accomplishment. With most people being undocumented throughout history, names could be much more fluid, like the way a person's "nickname" may change many times with or without consent.

No. There is not limit. That can by proven by seeing people with multiple middle names or by naming your child with multiple middle names. How could there possibly be a limit? Even with the case where systems can not store or recognize the length of such a name, the middle names themselves are not limited. People's names are not entries in a compiler's symbol table.

My son has two middle names (one for each grandfather), but he's still very much a minor and so not in very many "systems" yet.

(Although probably a lot more than I know about.)