The Rohirrim will name each other after each other.
They rarely have more than one name. (I have a hypothesis that names were given after the person was a few years old: like Éowyn – Horse Joy. Éowyn probably was a tomboy when she was a little girl, and probably loved to ride on horses like her brother. Thus her name.)
They have no family names.
Their names are always made of Westron, substituted by Old English/Anglo Saxon. Tolkien used Old English instead of Westron most of the time, so we can get away with it. Also, we know of so few words in Westron that we can’t properly make names from it. (41 PME)
The children’s names are constructed to sound like their parents’ names. A girl’s name will have some sort of common sound with her mother’s, and a boy’s name will have some sort of common sound with his father’s. Also, siblings often have similar sounding names. For example: Thengel→Théoden→Théodred and Morwen→Théodwyn→Éowyn. Théoden and Théodwyn are brother and sister.