By any other name?
First off: let's clarify something. Having a last name in Suikoden games is rare. Out of a cast of 108, maybe ten or twenty characters will have a last name. Having a last name is a symbol of the upper-class, that your family actually means something. For example, all the Zexen knights have last names, but the random Zexen peasantry are just Melville or Alanis. And when Caesar reveals that he's actually Caesar Silverburg, well, that's a moment.
So the fact that Nash has two last names is really something.
In Suikoden III, Nash introduces himself straightaway as Nash Clovis, and the added last name is probably meant to make him seem like a Person of Quality rather than a random sleazebag. When Percival, the low-born knight, calls Nash a ruffian, Nash takes offence. "I'll have you know..." His explanation is cut-off by invading lizard-people, but such are the hazards of Japanese video games.
But Nash is a Person of Quality. He was born heir to the house of Latkje, one of Holy Harmonia's most influential noble families. The Latkjes were at the forefront of the People's Faction, arguing for a friendlier, fuzzier Harmonia. As the Latkje scion, Nash was born into a world of privelege beyond that of the backwater Zexen nobility. He was supposed to carry on his family's political legacy.
That obviously didn't happen.
Through various events, both of his own doing and beyond Nash's control, the Latkjes are dead as a political dynasty. Nash might be a close confidant of the Bishop Sasarai, but when it comes down to it, he's a spy. Any effect he's going to have on international policies will be through stealing other people's True Runes.
There are a lot of reasons for Nash using an alias. Latkje might just scream Harmonia, the Clovis name might be harder to track, and maybe Salome only knows him as Nash Clovis or something. Certain parts of the Howling Voice Guild could still be after Nash, the Latkjes still probably have political enemies...there's no reason a secret agent wouldn't use a fake name. But maybe he doesn't want to think of himself as Nash Latkje anymore, maybe he just feels that his name ought to be as dead as his parents.
But Nash can't outrun his past or the Crystal Valley. In his blood, he will always be Nash Latkje, however much his tongue protests.
Really, though, I kind of think he goes by Nash Clovis because Latkje is too damn hard to pronounce. Latkje? What is that? It's like a cross between a Channukah treat and a veneral disease.