Only one can be used at a time, but it is definitely an interesting idea at its core.

The name makes Anakin start slightly, staring at the boy with a nonplussed expression. The idea that Leia of all people would ever name a child of hers for him... Luke, maybe--the more forgiving of te two, more like Padme in that respect--but not Leia. Not after everything he had done and stood for.

"I should warn you, then," he says after a moment, "that we come from different variants of the timeline. Han and Leia's boy was named Ben, where I came from." Implying there's only one.