As others have said, Wormtongue was more of a nickname given to him by people that didn't like him. Think Ivan the Terrible, Tsar of Russia, or something like that.
In fact, the only people in middle earth who are shown to have surnames are Hobbits and some Men from Bree, where Hobbits and Men live together and is no doubt heavily influenced by Hobbit culture.
I watch the extended editions every year and one thing that still confuses me is how at the start of the Two Towers Theoden has two Simon Peggs, and one of them gets savaged by a Warg on the way to Helm’s Deep; by this point in the battle he seems to have both Simon Peggs again.
What's great is this lesson can be taught to the world as "people with funny sounding names shouldn't be hired" which wow in that context sounds racist.