I'm a bit confused about how they get their surnames.
It's prefixed with Gro- (for a male) and Gra- (for a female), and followed by their father's name (for a male) or mother's name (for a female), according to UESP.net
But elderscrolls.wikia.com says this:
If an Orc leaves the province of Orsinium or Stronghold they're from, their surname will be the Stronghold/province they're from, prefixed with gra- (female) or gro- (male), for example, http://elderscrolls.wikia.com/wiki/Moth_gro-Bagol and http://elderscrolls.wikia.com/wiki/Ghorza_gra-Bagol (both from the same province).

So what's correct? Or how should a roleplayer create a family name for his orc?

The wikia is rarely correct. The strongholds are a new Skyrim-era creation, so while it's possible that Bethesda have changed the rules, there's no stronghold called Bagol, and definitely no province called Bagol.

Since Morrowind, Orc surnames have been a viking/Tolkien-style thing, where "gro" means "son of". There's no reason to assume it's been changed, especially based on some wikia user's theory which doesn't even make a bit of sense.

Thank you! From now on I'll just trust UESP.net.

It's not entirely unfounded. There's an Orc in Karthwasten, Lash gra-Dushnikh, daughter of Gharol from Dushnik Yal.

Then it's quite a fail of the lore writers.