As the BtN entry for Dexter says, the name is the same as the Greek name you describe. However, the name Dexter that is in common use in English-speaking countries comes from an Old English surname. It is pure co-incidence that the surname takes the same form as a Greek name.
♦ Chrisell ♦
All we have to decide is what to do with the time that is given us. - J.R.R. Tolkien.