Named after Admiral Sir Peter Warren, or his daughter Anne.
Anne, the admiral's eldest daughter, married Charles FitzRoy, later 1st Baron Southampton, in 1758; he owned and developed the land. Wikipedia names the admiral, Londonist names Anne – which would make this an unusual station name: neither Anglo-Saxon nor male. The station opened in 1907 as Euston Road, still seen in the platform tiling, and became Warren Street in 1908.