We have very little clue. The name was semi-popular in the last 1st century. It's possible it was a rich patron of "Luke", or, given that the name means God-Lover, it's also possible that it was a generic, everyman sort of address.

I have my own pet theory that Theophilus was a citizen of Pompeii, since we found the following graffiti there:

III.5.3 (on the wall in the street); 8898: Theophilus, don’t perform oral sex on girls against the city wall like a dog

Not really a view generally accepted by the scholarly community. It does show how relatively common the name was, though.