Having a patronymic surname (a name indicating your father) is but one possibility. There are also occupational surnames (like Miller), locational or topographic surnames indicating a place of origin or place of residence, descriptive names, etc. All are possibilities.

Remember that people did not always have inherited surnames (you bear the same last name as your father, and your grandfather, which you will also pass on to your sons). It's a fairly recent development, and came to the English speaking parts of Scotland long before the Gaelic areas.

Historically, you might have a second name that would give some information about who you were, so that you could be distinguished from others who had your same given name. Often people might use different second names in different situations.

One of the possibilities is to indicate who your father was. "I'm Robert, son of Donald," as opposed to "Robert, son of Gregor."

Another common practice was to give your occupation. "I'm Robert the Smith," or "Robert the Miller." You can see how in some situations this kind of information might prove more useful than who your father was. Especially if you were travelling in an area where people might not know your father.

Also if you had travelled, letting people know where you were from would be common. Saying, "I'm Robert from Glasgow" wouldn't mean a durn thing in Glasgow. But if you travelled to Inverness, it let's people know where you were from.

Some second names were physically descriptive. Robert the Red ("Rob Roy"), or Robert the Long (Lang), or Robert the Younger (Og), would all be examples. The point is simply to distinguish you from others with the same given name.

And you will occasionally encounter names that combine some of these. The name "MacGowan" means "son of the little Smith." So there were have a patronymic name that carries with it not only an occupational name, but a descriptor, as well.

Remember these were non hereditary names to begin with. But over time, when people started to use hereditary surnames, many of these turned into the surnames we know and use today.