Marriage: How do names work?

I am currently engaged to be married, and I have just realized I have absolutely no idea how the whole names thing works. Maybe it is because it works differently here in Spain to the UK, and as those are the two cultures I know best, there is some confusion.

When a couple gets married, I know that there is something that happens with family names, they change or mix some how.

How do names change when there is a marriage?

Is it optional? are there alternative versions?

How do name changes affect any future children?

Is it possible to share names, rather than anyone lose a name?

What are all the options and alternatives?

I know this is probably a silly question, and the answer is probably obvious, but I am confused by it all. I know my English mother lost her last name and had it replaced with that of my English father, but in Spain it seems to work differently, as my friend has the surnames of both his father and mother, while I only have my father’s surname.

Thanks.