Well, it depends on the ethnicity/culture of the orphan. I have a rather vast world with many different peoples, and it varies between them.
For the Kithnarya/Eya, it depends on which they are firstly (the Eya are Kithnarya, but not all Kithnarya are Eya – a good comparison would be Irishmen versus Irish Travellers). If the child is Kithnarya, they will typically be named after their place of origin; an orphan from Khorasan would have the name Khorasanya, one from Alamut would have Alamunya, etc. It’s less of a surname and more of an epithet/demonym meaning ‘one from Khorasan’ or ‘one from Alamut’.
For the Eya, as they travel and rarely have a city they settle down in, the child is usually adopted and takes the name of whatever family adopts them. For example, one of my MCs, Nadia Fabian, inherited the Fabian name from her foster family instead of her actual surname by birth (Dyani).
For the Northmen, they are often given a very simplistic surname, such as Snow or Stone or River.
For the Bellans, the ward (as they are called) is given a name based on the fief they are a ward of; one of the main Bellan characters is a young man who is a ward of Ravenwick March, so he is known as Avatus of Ravenwick. Until his actual parentage is learned, that is, and he gains his father’s surname.
"Remember, you go nowhere by accident. Wherever you go, God is sending you." - Rev. Peter R. Hale