Hilton loved the Christmas present, Richie told Saturday's New York Post.
"Rats make great pets," she said. "They're cute and when they nibble on you and crawl on your shoulders, they're fun."
Spelling's reaction, however, wasn't as loving.
"I told Tori I named my rat after her, and Tori said it was funny, but I could tell it hurt her feelings," Richie said. "She must've felt I thought her face looked like a rat's, but I actually own six rats, and what she didn't know then was that I've named each after a 'Beverly Hills 90210' character like Shannen Doherty and Luke Perry."