Thank you all. I'm a native Polish speaker as well - and indeed we don't have one name for a tea-cup handle. We call it, as elifit pointed out, a tea-cup ear (or just an ear).

I just thought, perhaps unfairly, that 'handle' is not the most elegant English word to use in this context. And also, since English has a loooong history of words borrowed from other languages, I almost expected there to be one even if not of English origin (there is one in Welsh!). So you're right, there's a lesson in it for me...

Best,
Rafal