In this episode, when Lorelai goes to visit Rory at Logan's apartment, Rory asks if she took Christopher's name, Hayden and Lorelai says: "No. No. "Hayden"? No. I don't want to be Mrs. Hayden planetarium for the rest of my life. I'm Lorelai Gilmore, okay? Lorelai Gilmore without the "Gilmore" is like... Gil, you know, less. Okay." But in the previous episode, French Twist, when Lorelai and Christopher arrive home, Chris tells her: "Welcome home, Mrs. Hayden.". Probably the previous episode is the wrong one, because we will see Lorelai using Gilmore on the episode 'To Whom It May Concern.'
Possible explanation: Because they rushed into their marriage, they probably hadn't discussed the name change issue. Christopher calling Lorelai Mrs. Hayden was perhaps just the giddiness newly weds feel after their wedding.