From the experts:
One of the few ancient Roman names that doesn't end in us, the rarely heard Tarquin has a decidedly creative, even dramatic flair, which could appeal to the parent looking for a strikingly original name. Sir Laurence Olivier used it for his oldest child, who was named Simon Tarquin but called by his middle name.
As Tarquinius, it was borne by two early kings of Rome.
Tarquin has some literary cred as well, appearing in Shakespeare's poem The Rape of Lucrece (referring to a dark stain on the name), as Tarquin Blackwood in Anne Rice's The Vampire Chronicles series and as Tarquin Cleath-Stuart in the Shopaholic series by Sophie Kinsella.