That is indeed what most places do: the names are a more recent thing. Of course, now you need to keep the paper receipt with the number on it, or a plastic number card that might or might not be returned to the counter, then train yourself to listen for an arbitrary number, even though your brain is already quite adept at hearing your name. For most people, most of the time, the first name is an upgrade. For edge cases, unfortunately, it's worse.

One restaurant I love approaches the problem by giving out name cards (brightly-colored paper, so disposable or cheaply replaceable) rather than numbers on the receipt, but the names are of famous personalities. I've been Dolly Parton, I've been Arnold Schwarzenegger, I've been Jackie Robinson, etc. They're fun because unlike numbers, they're easy to remember and can provoke conversation in a group, or fond thoughts when alone. Bravo to Twisted Root Burger Co for this approach!

You'd need a ticketing system so people even remember what their number is. And for what upside when names work fine?