TRY TO ... (I'm quite new as well - but the MOD's seem 2B "trang" ;) : "Tha mi" would be our simple "I am" (Ich bin) but "Is mise" would be more emphasized on the "I"/ on the "me" aspect - as in "MY name is" (MEIN Name ist) - just like "Please listen to ME, because MY name is" ... does THIS make sense to you ?!
The other poster is correct in the difference between mi and mise. According to Wikipedia, "tha" is used for temporary states, locations, etc and "is" is used for permanent states. I'd imagine that if one changed one's name it'd be "Tha mi Iain a-nis" when before it was "Is mi Seumas"