Love how the question was for girls yet other than me it was all boys who answered lol.
Was it really a how do you as a girl think question as much as a clearly observable stats and law/societal customs question?
Anyway.
Traditionally in the UK one would change your name (probably a legacy of Roman Catholicism but I will have to look that up, to that end it would extend to a lot of Europe) to that of your husband if doing the whole marriage bit. As marriage was traditionally viewed as important then yeah.
There are a few cases of double barrelled names being made, mostly in the cases of massive class differences or upper class politics, or if the last of a "notable" family line only had daughters which would thus make the name die out if they got married.
Today if marriage is a thing (marriage rates among younger people in the UK are crazy low these days, cohabitation very much being the norm) some do remain with their maiden name or create a double barrelled name. While it would be tolerated under "do what you want" don't be surprised to find it seriously looked down upon by people old and young (very much so old though), have your potential husband get the piss taken out of them and people assume things about you and your approach to the world. I can well see it being a dealbreaker for a man as well and you won't find many in the general population that look down upon them for that. While I can't rule out a man changing name today it would be exceptionally rare, and again much would be assumed (none of which being that said man was forward thinking and magnanimous) about their personality or that they are trying to get away from something (though why marriage would be it rather than deed poll is a different matter).
Professionally you may also be known as something else -- I had a few teachers change but others remained "for consistency", on the other hand quite a few people that spent years making a reputation as one name and keep that professionally. Even knew someone get married, change name, graduate and start doing things professionally but then divorced but keep the married name professionally and personally for many years. They later got married again and kept the first married name professionally until they left the country (it being the main reason for the second marriage) and could "start over" as it were with the new surname.
Divorce wise some will return to their maiden name, some will continue on with their married name. Same for death of partner.
There is a little used term these days called "née" which serves to allow people to note both names, ex. Jane Smith née Jones. One tends to only see it during funerals these days though, or maybe legal matters.
Among the gays. Not sure offhand about hard stats. From what I have seen then if it is not a mouthful then some do double barrel, others remain the same, some even create a new surname. You don't tend to see the gays change beyond double barrel though.
I saw the security question mentioned. I do find it odd when people could go on facebook, find your mother's brothers and go from there. Also with the amount of bastards in the world nowadays (me being one) it gets odd so some instead ask for your grandmother's maiden name. The case of bastards and living sperm donors and what names they get given is also a fun one (I looked into it a few years ago and there are no laws or assumed things that I could see), though actually not as fun as the older takes on such things (is there a family matriarch, or a family patriarch, they will probably be deciding, and you also have the case of people marrying wanting to claim their bastards or indeed random children). In the case of subsequent marriage with older children it can also vary, typically I would find it depends upon the position custody and of the father (if they were an abusive arsehole then don't be surprised to see a change, if they are living and still liked then change is unlikely, if they are dead it is a toss up between their memory and other factors).
If you want a fun case of family names/surnames I suggest looking at Iceland.