Which admiral gave HMS Rodney her name?

Was HMS Rodney named for the admiral who relieved Gibraltar?

Yes. The battleship honored Admiral George Brydges Rodney, one of Nelson's heroes and a major influence on the Royal Navy's later officer culture.

HMS Rodney commemorated the admiral whose convoy and victories helped sustain Gibraltar. Rodney is described as at least comparable in quality to Nelson, who regarded him as a hero. Rodney and John Jervis, later Earl St Vincent, helped school many of the officers who led the Royal Navy in the next generation. The name recalled both a particular commander and a wider tradition of fleet leadership.