And gupta is from a root meaning to protect (so gupta is protected). I am not clear on the Indoeuropean cognates of this root, and many of its derivatives can be confused with the derivatives of go (cow) + pA (protect/raise). In later language, the root gup only survived with a meaning `to hide'.
gupta is the last part of the name of a very important dynasty of emperors in India. In fact, the name Chandragupta (Chandra is moon) appears even in a previous dynasty. But, the so-called gupta dynasty started using the -gupta bit dynastically: they named their sons (at least when they became kings, they had the name) ending in this. You can read more about them in my history of bengal pages: http://tanmoy.tripod.com/bengal/earlyphase.html#gupta
though I am sure google can get you more relevant links on this dynasty.
Many smaller rulers and noblemen descended from them and still carry that name. I do not know if all guptas are related, or at least claim to be related. In bengal, gupta also forms part of compund surnames (sengupta, kar gupta etc.)