While his paternity remains a mystery, January Jones didn't keep her son shrouded for long, debuting one-month-old Xander yesterday at a doctor's office in Beverly Hills.

And he is adorable.

MORE: January Jones' "Son" Calls Her Mean

The 33-year-old Mad Men star gave birth to son Xander on September 13 but previously discussed her dilemma when it came to choosing a name for her then-gender-unknown child. "I'm having a hard time. I'm looking for boy and girl names obviously, because it's going to be a surprise for me. I love Cary Grant, I like Marilyn Monroe. That seems kind of like a celebrity thing to do, those weird names. I'm not really into that. I don't want to be too cliche about it."

January also revealed her biggest pregnancy craving: Dairy Queen! "I was just home visiting my family in the Midwest and I went, literally, every day," she told People. "I made my dad take me. Pregnant or not, I love Dairy Queen. I usually get a cherry-dipped cone or sometimes I go for a Blizzard and a chili dog if I'm really hungry."

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