I have to agree.
Chloé is always CORRECTLY pronounced "Klo-AY". If you ever get any close to
France or a French speaking country, you better be prepared to be called "Klo-AY" all the time, as this is the original French pronunciation.
If it really bothers you so much, you should just correct the spelling mistake and stop using the accent. It shouldn't even be a problem to legally change the name, as it was just a mistake and it bothers you in your daily live.
You cannot use Chloé and insist on the English pronunciation, that is quite ignorant and there is no way people can know and they will always continue to say "klo-AY" (and they are right).
Personally I prefer the French pronuncation to the English one, I think "Klo-ee" is way too cutesy and reminds me of an "eek" kind of sound.