[Facts] Re: Anjezë (meaning) and Mute (a name which has that as its meaning)
I guess you could try something based around 'aphasia'? You might not get anything that is -actually- used as a name, since, as has been pointed out, names with that specific meaning which can be used in a European, or Italian, context are pretty thin on the ground. Something like Afasia might work? Or you could use the roots 'aphatos' (speechlessness) or 'a-'(not) + 'phasis' (speech) to make a name? I mean, a lot of European/Latin/Italian names actually do come from Greek roots, so it's not too insane, I guess. I guess it doesn't mean 'mute', more, 'not able to speak for neurological reasons', but...
Ooohhh, what about Aphonia? 'Phone' is a pretty common Greek name element, it fits with the 'mute' element more than Aphasia, and it does look kind of name-like. Come on, if Alexia can be considered a name, why not Aphonia? Or, since Eulalia is a name, and Dysnomia has somehow come about as a rare name, what about Dyslalia?