The name of several Starfleet ships, including the Excelsior-class Hood on which Riker served as first officer under Captain DeSoto.
Several Starfleet ships have carried the name Hood. A Constitution-class USS Hood took part in the war games with the M-5 computer in the original series episode The Ultimate Computer, during which it was damaged by the Enterprise under M-5's control.
In the twenty-fourth century, an Excelsior-class USS Hood served under Captain Robert DeSoto. Before joining the Enterprise-D, William Riker was DeSoto's first officer on the Hood, and Picard picked him partly because he had once refused to let DeSoto beam down to a dangerous planet, Altair III. The Hood appears at Farpoint Station in Encounter at Farpoint and again in Tin Man, where it delivers the Betazoid specialist Tam Elbrun to the Enterprise.
Riker did turn down offers of his own command during his years on the Enterprise-D, but these were for other ships, including the Aries and the Melbourne, not the Hood.