I changed my name on marriage and my DC had his name. I would never now recommend anyone change their name on marriage and never ever have a different name from your children.
ExH turned out to be emotional, financially and eventually physically abusive. There was no signs before marriage or really before the birth of our first child.
I tried to continue with ExH name but eventually I did realise I had to change it. ExH wouldn't allow the DC to double barrel. Court agreed with him, he needed children to carry on the family name apparently (yes this was in the courts summary). So DC have a different name.
Every new hospital consultant/doctor therapist (and we have a few) calls me Mrs Violent ExH, I do correct them but it makes me look pedantic. letters are often still addressed to Mrs Violent ExH. I cant count the number of phone calls that have gone "please can we speak to Mrs Violent ExH?" "Do you mean (DS' name)'s mum" "yes". This is across multiple hospitals no matter how often I correct it. Schools do generally get it right once corrected. I dont really care so much anymore, but at the start it was rough.
Travelling wasnt too bad at the start but it has got progressively worse over the years. These days I am asked for Birth Certificates nearly everytime I return into the country with the DC and the DC are (briefly) questioned most exits. It's ok but not what you necessarily want to be dealing with. Customs officers have actually checked the physical copies of birth certificates, marriage certificate, decree nisi and deed pool, all of which I carry every time. Pictures on your phone wont necessarily cut it. I have even very unpleasantly told off by a customs officer for travelling with genuine copy of a birth certificate (given to me by the registrar when i registered DC) not a certified copy. The difference? one says "certified copy" and has a seal, the other says "genuine copy" and doesn't. He really does stand out for being a git though.
Of course the worse thing is that DC have been lumbered with the surname of someone who was violent towards them. Mainly because noone wants to remind him we exist by asking (again) his permission to change it. Eldest DD is counting down the days until she can change it without permission.
I know our story isnt the norm, but it does make a salient cautionary tale. If heaven forbid it all goes horrendously wrong putting it right after the event is a hell of a lot harder than getting it right the the first place.
You keep your name, kids get yours (or compromise on double barrel). Never ever give your kids a surname that doesn't match your own.