Lets think it through. You're Jane Smith, you move away to uni, meet someone, get married at 23, become Jane Brown. Move to a new town, have a couple of kids. It all goes to hell and you divorce at 28. Keep the same name as the children. Meet other school mums, friends from work, etc. At 33 you remarry, change your name to Jane Newhusbandsname, then that fails after five years.
By this point you'd been Jane Brown for 10 years, and Jane Newhusbandsname for 5. Your kids are the Browns, some people at school still assume you're a Brown because of them, most people who know you as Newhusbandsname knew you first as Jane Brown and literally nobody in this town has ever heard of Jane Smith.
So... why wouldn't you just go back to being Jane Brown? Then, with a new partner, well you've bloody well learnt your lesson from messing about and name changing, not to mention the pain of going to the school and being a different name to your kids, so you are a) never going to get married again and b) never going to agree to have your children have a different name to you again. Its possible if you could have your time over you would have stayed Jane Smith from the start, and pushed for the kids of be Smith-Browns or just Smiths, but you didn't so you have to work with what you have.
As I say, in my scenario, I haven't changed my name, neither has my husband and our children will be double-barrelled. But if I was Jane Smith originally in the situation above, I think I'd probably end up where she has.