The fact that you yourself don't know how you would pronounce it is a sign to me that this is a bad spelling. Not that I'm totally sure that pronunciation you're trying to get across by "
Have'n." If you want to name someone
Haven or
Heaven, just name them that. Then people will know how to pronounce it. The purpose of the way a word is spelled is to tell you how to pronounce it. (Though I also don't really think
Heaven is a reasonable pronounciation of Havyn.) Pronunciation aside, I don't ever really like alternate spellings to word names. I think they universally look silly and uneducated.
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https://www.behindthename.com/pnl/120652