I'm pretty certain that the name "Spartacus" is derived from the Latin adjectives "spartiaticus" and "sparticus", meaning "Spartan", but I'd like to check a few more comprehensive Latin sources when I'm at work later today. Likewise, I'll check into those other Roman names.
"Rembrandt"... I know that the "-brandt" element in Germanic names means "flaming sword". Not too certain what the "rem" element might indicate in this case. In many names, the "rem" is derived from "regin", meaning "counsel". Do you have any ideas?
-- Nanaea