Of course we can't be sure why Shakespeare chose the name Hero, since he did not leave analyses of his works behind for future scholars to reference. Maybe this is why we have more research and analytical writing about Shakespeare's works than most any other author.
That said, there is no mistaking the reference to the mythical priestess Hero loved by Leander. Their story is quite a famous one in Greek mythology. This Hero had taken a vow of chastity as a priestess of Aphrodite, and Leander died as a result of pursuing his love for her. Ironically, if the Claudio of Much Ado About Nothing had been familiar with this myth, he might have been a little more hesitant to accuse Hero of loose sexual morals. Since Christopher Marlow wrote a poem concerning the lovers Hero and Leander around the time we suspect that Shakespeare wrote Much Ado, this could account for his interest in the character name "Hero."
There is also reason to consider the more general meaning of "hero" as it is generally used in any story. The "hero" is the character who endures trials and tribulations throughout the tale and who emerges victorious over his struggles in the end. Usually, "hero" is considered a masculine term, while "heroine" is the feminine equivalent.
In the Comedy Much Ado, it is certainly Hero who endures and suffers trials and tribulations and emerges vindicated and victorious in the end, and, since she is conventionally feminine in her demeanor (in contrast to Beatrice), it could be a bit of an ironic twist by Shakespeare to use the masculine form of "hero" in naming her.
For more on Hero and other meanings of the word, please follow the links below.