As we've seen with The Doctor and Moriarty holoprograms can become sentient. If someone were to recreate a deceased person accurately enough that the program becomes sentient, would that program be considered the same person as its model?
Though to be honest the whole holoprogam sentience thing got blurry after TNG. The Doctor was sentient yes, but were Zimmerman's other holograms? Were the other EMHs also sentient? It gets confusing because of the way that holoprograms begin to act. In DS9 the holoprograms seem to be self-aware in the fact that they are holograms. Where is the line drawn?
Nobody on DS9 considered Vic Fontaine as sentient even though he was believable enough that they emotionally connected to him as if he were.
The program would not be the same person as its model. It would be a new individual, who behaves very similarity to the original.