Guy Kibbee played the title role in the 1936 Shirley Temple movie, Captain January.
I’d rather like to forget it, but:
Dr Christmas Jones, as played by a cardboard cut-out of Denise Richards in The World Is Not Enough.
Years ago, Burt Reynolds played a TV detective named Dan August.
Well, Ruby Tuesday was a character in a Rolling Stones song…
And, in passing, I’ll mention that author Julian May (mentioned above somewhere) is a woman, not a man.
Or maybe I was being whooshed.
Out of the pool! And take your giant foam noodle with you!
As far as real people go, there’s always Tuesday Weld, subject of that great (well, by his standards) Fozzie Bear joke: “If Tuesday Weld married Frederick March’s grandson, she’d be Tuesday March the Second!”
Or the Pinky and the Brain Are-You-Pondering-What-I’m-Pondering:
“I think so, Brain, but Tuesday Weld isn’t a complete sentence.”
Carl Enders in Windtalkers?
If Christmas counts, then Joe Christmas from Light in August. And I don’t remember Nadine Gordimer’s July’s People all that well, but I seem to recall that “July” was only called that by his employers, so that might not fit the OP’s criteria.
Oh, and I think the two main characters in Chaucer’s “Merchant’s Tale” were January and May.
How very true. However, I read the thread title as:
Characters Named After The Calendar
There’s a seven on every page of *my * calendar. YCMV.
Augustus Gloop
psst. tdn. Read the last line of the OP again. 
From the same novels (I think, I don’t have them here to check) her mother Wednesday Next and her son Friday Next.
His wife was Queen (Sara) Saturday and their son was Prince Tuesday (who actually was born and grew up during the series). In the never resolved cliffhanger, Saturday and Tuesday and Friday, Lady Aberlin and Lady Elaine Fairchild were all tied to chairs in a basement as the People’s Republic Under Comrade General Striped Tiger was debating what to do with them “and any other idle rich blood drinking aristocrats”.
One of the Three Investigators books I read as a kid had a character named August August.
Baron Samedi from that Bond movie.
Captain Pike in Star Trek was Almost named Captain Robert April, Captain Winter or Captain Spring.
cite: Christopher Pike | Memory Alpha | Fandom
A character named Captain April turned up in one of the cartoons.
Captain Kirk was almost named Captain January.
cite: James T. Kirk | Memory Alpha | Fandom
Ah. Now I can post what I was going to post last night, just before the board went kablooie.
Yes and no. There was a July in the book (and the movie as well) but she wasn’t named after the month. She was left with a note from her parents asking that someone take care of their daughter July…“Probably, they meant “Julie,” but July she was named and July she was called, like the month.” (It’s been 20-some years since I read it, too, but I still have bits of it in my head.)
There’s also Tom Sunday from Louis L’Amour’s The Daybreakers and Gideon Sunday (and his sister Tuesday) from the book Blood River Down.
How is that a calendar name?
Samedi = Saturday in French
Merci!
I’m embarrassed to admit this, but I remember reading the book. There’s a bit in it that goes approximately: She claimed she was born onthe 4th of July, and they would have had a party for her on that date, if they had been allowed birthday parties.