If I change my gamer tag will it affect anything my Microsoft account is linked to?

Changing your gamertag does exactly that, changes your gamertag. The account and everything attached to it remain the same

I had the same question and I am glad that you guys were able to answer it. Thank you. Good Day!

I mean changing my current tag to a new one, I'd just like to make sure it won't affect the Xbox Ambassador programme or anything like that.

If you are just changing the gamertag name
on the existing account, it will not affect your achievements, in game progress or game saves in any way - all it does is change your name (at a cost of course). But if you
are just making a new 'tag then yes, everything would be lost and nothing will transfer over.

You can switch without fear! The most important thing about your account is not your gamertag, but your email.