What is a different way to spell "harmony" to make it unique?
Perhaps "harmani" or "harminee"?
If you're going for something like a band name, then your options are to consider other letters (or letter combinations) that make the same sounds in the word.
Phonetically, "harmony" is spelled /ˈhɑr mə ni/. The consonant sounds /h/, /r/, /m/ and /n/ really have no substitutes, so your best bet is to replace the letters that represent the vowel sounds /ɑ/ /ə/ and /i/.
The schwa /ə/ is the easiest to replace, because all the English vowels make the sound from time to time. Try replacing the "mo" in "harmony" with "ma", "me", "mi" or "mu".
The /i/ sound is also fairly easy to replace. Try replacing "ny" with "ni" or "nee".
As for the /ɑ/ sound in "har", the only English vowel that can really make that sound is "a". Unless you want to make it "aw" or "au", I'd think it's best to leave it at "a".
Try playing around with different combinations of these until you get something you like.