I believe you're looking for a credible reason for a naming convention. Some samples below of how surnames came into being.
Traditionally, surnames were given so that a town's individuals with similar names could be distinguished from each other. Smith is an obvious one. Wainwright, Cooper, Johnson, and so on. Another convention before a statutory surnaming convention served government purposes for censuses, taxation, law enforcement, and military conscription needs was to surname a person according to some distinguishing circumstance.
Appearances, apparel, accessories, weapons, jewelry, decorations, and tatooing, daring deeds, foolish acts, place of domicile, and so on, some unique and memorable identifier, more nicknames than surnames, nonetheless they were useful for identifying persons by surname. More precisely, they are synecdoche or metonymys. In the far back, no one had much more than that and often only as a given or taken name. We see the like today when a person's taken name is all he or she might go by publicly. Some even legally change their names to one word or simple phrase identifiers. It's tribal naming conventions that follow that principle.
What I'm getting around to is solely a given or taken name might fit the setting, especially the time and place for high fantasy. Working that into the narrative might enhance setting and go toward situation and character in terms of self-identity and projected identity. Also, changing names was at one time a feature of coming of age rituals. It still survives in religious institutions for taking a name of a saint, prophet, or martyr at ascendance rituals. And taking new names for passage rituals is not uncommon even today. Birth name, baptismal name, confirmation name, each added on, in turn, and adding to a person's statutory identity. The marriage ritual traditionally changes a woman's maiden surname, though that practice is under revision, rightly so in my opinion.
Spanish naming conventions respect the personages' surnames of one's lineage that are of the aristocracy and in position according to pecking order. Don Juan de Velasquez de Alyon de la Maria Santos, for example. Typically male lineage first, then female, unless the female house is of higher station.
My given name and surname translated from the original languages into contemporary parlance means first born of moonlight stalker. Some of which is valid to my self-identity. I'm not first born of my sibling sept though. I do tend to hunt through the moonlit darkness of knowledge, however.
Spread the love of written word.