Everyone first name is music to their ears. I wouldn't change it. That having been said, here are some things to consider.
"Ben" is a common name. It is short for "Benjamin". (I understand yours is not; just stating a fact, but see below).
"Pen-pin merger": Many Americans pronounce "pen" /pɛn/ and "pin" /pɪn/ the same (/pɪn/) unless they are speaking carefully. The name "Ben" and "Bin" would probably be pronounced about the same. Some speakers may say /bɛn/, others /bɪn/, but generally, it would be easy to pronounce for them and not at all awkward.
"Vin" is less common than "Ben" (Bin). It sounds like it is short for "Vincent". It's a fine name either way.
Unusual spellings indicate to the reader that maybe normal English "best effort" phonetics don't apply. If you write something like "bhin", "bheen", "bihn", etc. the reader may interpret that as "Pay attention: there may be some unusual sound here!" and give some unexpected response. If they are reading your name from a document, they may raise the tone of their voice as if asking a question, waiting for you to pronounce it for them correctly. If you wrote "Ben", "Bin", "Vin", etc. absolutely nobody would stumble.