My understanding was that the two domains are equivalent. The following sites seem to confirm my understanding. Are you sure it isn't you?

https://support.google.com/mail/thread/125577450/gmail-and-g...

https://www.quora.com/What-is-the-difference-between-gmail.c...

https://www.gmass.co/blog/domains-gmail-com-googlemail-com-a...

I'm pretty sure I don't have an alter ego who lives in the UK ;) The shipping address and accounts opened by this person are very obviously not mine.

I live in NY.

Was there a period where you could register those separately? My old google account receives emails for both domains.

There must have been, else I wouldn't be in this situation.

Or they could just have a similar gmail address they frequently get wrong (or that looks like yours when written in the terrible handwriting they fill in forms with)

There's probably a single digit number of people with my initial and surname in the world, and I still get order confirmations for one of them, car promotions for another and am on some sort of targeted B2B spam list for a third to my Gmail address in that format. I quite like the order confirmations tbf, most of them are for a fish and chip shop I actually used to get food at when I was a kid and my grandparents lived nearby so they're oddly nostalgic

it's the exact same email, only with "googlemail.com" as the extension.

Nah, this person just doesn't know what their own email address is and types yours instead (yours with googlemail). This happens all the time and it really isn't something Google can do anything about.