No it's not right, the right thing to do would be to contact the local network provider as they should be able to track down onwership.
However it's up to you what you do with it.
I know I'd return it because that's what I'd hope someone would do with mine if I lost it, and I believe in Karma.
BTW, you should be able to find the phone number by checking the options, most phones have owner details or at least phone # in it.
Of course it could be a disposable phone from drug dealers, in which case have fun with your new phone but don't be surprised if someone is listening.