His full name was Theodore Roosevelt Jr. named after his father Theodore Roosevelt Sr. who lived from 1831 to 1878.
He actually seemed to dislike the nickname "Teddy", and had a history of condemning people who called him that. He does not protest when Xavier calls him this though. Perhaps perplexed by how Xavier talks about his mustache.
He was married to Alice Lee in 1880 until she died in 1884, then Edith Carrow from 1886 until his death.
Xavier actually compliments his mustache immediately upon meeting him in 1865, even though at less than eight years old, he probably would not have any facial hair since he would not have started puberty. A photograph of him at eleven years old showed him bare-lipped.
Teddy notably does not say anything when Xavier mentions this, but looks down and wiggles his lip. It's unclear whether or not he can actually see a mustache there like Xavier can.