What is the scientific name of the daddy long legs spider?

It depends what species you are referring to. There is the crane fly. It's scientific name is Nephrotoma.

You are probably referring to the cellar spider or the harvestmen. The cellar spider

is most likely the spider you are talking about. It's scientific name is Pholcus phalangioides. There harvestmen's scientific name is Hadrobunus grandis.