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No, this is wrong.
The original title was "Mai-HiME", and that's because the character is named Mai, so the title titles (no pun intended) her as both a "hime" (princess) and a HiME. And it's a pun on "my", as in the possessive first person pronoun.
But by translating the name as "My-HiME", you lose the connection with Mai, and have to bootstrap up the pun on her name in reverse. It also puts undue emphasis on the possessiveness.
I prefer this alternative: "Mai Princess". This way, you're translating the "hime" part, describing Mai as a princess, keeping the pun on "my", and all you need to do is to have fun with acronyms until you can find something to fit "PRINCESS". Possibly in CamelCase.
Comments
Doesn't "maihime" also mean something though?
Or they can just call it Mai-HiME or My-Hime or whatever, because all things considered, translating puns in titles is just about the least important thing and all that really matters is that people can identify it easily.
And leaving the title as "Mai-HiME" would be better than calling it "My-HiME".
My-HimePrince