In an interview with Vanity Fair several months ago, Amy Sherman-Palladino told fans that Rory would be dating in the Gilmore Girls revival, but her situation on the Netflix series is a bit more complicated than I imagined. Who is Paul in Gilmore Girls: A Year In The Life? Rory's new (ish) boyfriend is played by Jack Carpenter, who played Dash in The Return of Jezebel James, an Amy Sherman-Palladino sitcom that was cancelled by Fox after only three episodes. There are spoilers for Gilmore Girls: A Year In The Life ahead, so you might want to cancel your plans and finish the episodes before reading.
Paul shows up in "Fall," and we learn that they've been dating for two years — which is a significant amount of time. However, he hasn't made any impression at all on Luke, Lorelai, and Emily. They can't remember his name, or having met him before. Even Rory forgets about their dates or even when he's there with her half the time. It's kind of a running joke with his character, much like how Rory is always on her way to catch a flight in the new episodes. How can she afford to jet everywhere with no steady job? Unclear.
Anyway, Paul doesn't have much of a personality, or a last name. He seems to be handy at fixing things, but that's about it. He follows Rory around like a puppy in "Winter," is not seen and all in "Spring," and she keeps meaning to break up with him but never follows through.
There's also the small fact that Paul and Rory are in an open relationship without Paul knowing it — or, to be extra clear, Rory is cheating on Paul with Logan whenever she's in London on business. That's definitely a problem. Classic Rory Gilmore, totally unaware of the damage she may be causing on others. Poor Paul.