Never been an issue for me.
One of DS's middle names is my name. I wasn't going to lumber him with a stupid double barrelled name in the name of equality (how the hell are the double barrelled children of today going to navigate it when they marry - its a STUPID 'solution').
Its fairly obvious we are related because its his middle name.
If DH travels alone with DS he'd be wise to be able demonstrate DS is allowed to leave the country with my permission anyway just because of how many divorced parents there are.
Again this idea is a STUPID one to change your name for.
There are so few pros to changing your name.
I am often called Mrs GreenToothBrush by people who don't know. I generally don't correct in social circumstances cos its not necessary and it doesn't bother me. On paper work I just use my name. Cos its my name.
Its useful for identifying salesmen / telephone sales and prickish political canvassers (who have a list of residents for a house, know my husband's name but can't be bothered to have the courtsey to use mine when they have it right in front of them).
The only issue I've had is with Nationwide telling me it was illegal to NOT change my name. I rolled my eyes and no longer bank with them due to that and other reasons related to terrible customer service.
DH wanted me to change my name and was really insistant about it. I told him I couldn't be bothered with the hassle. He got over it very quickly and its a complete non issue now. He doesn't even remember being an arse about it to the point that he insists he was 'fully supportive of my decision' (he wasn't!).