There is nothing wrong with using an alias on a dating site. A good number of people feel uncomfortable using their real names on public platforms such as dating sites.
If you want to use a fake name, it’s best to use another common name. It just makes it easier for a potential match to take you seriously.
If you use an obvious fake name like “Batman,” some potential matches may pass on you because they might think that you aren’t taking online dating seriously and for all they know, you may have a dating profile up just for the fun of it or for a good laugh.