"redial" -- ask whomever it calls who owns the phone
"call mom" or dad or any number of common names
"dial 1234567890" substituting your phone number so you can see the caller ID and then google search the phone's phone number to see if you get a hit.
Keep it powered up and where it has cell service to see if the owner puts it into Lost mode with a message.
Beyond that your best bet is turn it in to the police and advise the management of the place where you found it that you've turned in a phone. May not ever make it to its owner but you'll have at least made an honest effort.