I think it’s not so much that “Jones” is formal as it is that “Bob” is explicitly informal.
I am one of very, very few women I know, perhaps the only woman I know, who goes primarily by my surname–and even though that’s honestly what I prefer, half the adults I know still call me by my first name. Part of it is that as a teacher, I go by Ms. Surname a lot, and I don’t really like that: it’s too formal. I can’t really have students call me by my first name–that’s too informal. So Surname it is.
I also just like my Surname more than my first name: “Amanda” is very feminine, and while that’s not bad, I think it has connotations I don’t live up to or down to or whatever. It has never felt like my “real” name. My surname, on the other hand, is very unusual and very cool (IMHO). That’s largely why I kept it when I married.
But it takes a couple years for new members of the faculty to grok that I really do prefer that, and quite a few never do. If I get introduced to someone by someone who knows me by last name, it usually sticks. Outside of school and school-related, like with my son’s friends’ parents, I just go by my first name. Not worth explaining or trying.
My husband calls me “Mandy”, the name I used when we met. At this point, only he and my family and very old friends use it. I call him by a diminutive of his last name, ironically.
But yeah, I think surnames are coded as somewhat masculine, and it’s vanishingly rare in my experience (and I pay attention) for a woman to go by her bare surname preferentially.