I am thinking about getting a completely different apple id when I get my next iPhone. I don't have a paid developer account. Or do they actively prohibit multiple accounts? I've never tried on Apple before but I have multiple goog.e accounts and it seems fine to have different accounts on different Android devices?

Moreover on Android you still can have 10 different Google accounts on one phone all from different countries for downloading region-locked apps on Google Play. Though recently Google started to break it by changing account region countries nilly-willy. Yet you can still register as many accounts via Chrome as you wish really without extra gmail accounts just by using own domain redirect via cloudflare or something.

On iOS installed apps are locked into specific Apple ID they been downloaded with, so you might have issues with e.g WhatsApp. Still possible to download region-locked apps with non-primary AppleID, but it will sometimes ask to re-authenticate with said AppleID to keep it updated so it's cant be just throwaway.

You can have up to three IDs per device.

https://support.apple.com/en-us/101661

That's consumer electronics. They're toys.

"Can't change it" means "haven't tried to change it". People's legal names change, so you have to be able to update a record of your legal name.

They told me they would need a notarized letter signed by both me and my mom. I figured at that point I’m just gonna die with this account name.

That's not actually hard or anything. Notaries are all over the place.