updated 01/30/2012 AT 10:00 AM ET
•originally published 01/30/2012 AT 3:45 PM ET
J.R. Martinez and Diana Gonzalez-Jones, who are expecting their first daughter in May, have narrowed the names to two. Expect something special – but nothing absurd.
“We won’t name her Apple Cider or Salami,” the Dancing with the Stars champ, 28, vowed to PEOPLE at Sunday’s Screen Actors Guild Awards. “It won’t be our favorite dish or our favorite getaway or favorite car or show.”
So, what’s left after that? “It will be something really close and personal to us that feels like we’re giving something to her that is very special,” he says.