So do you mean what Admiral Cecil did to warrant having the destroyer named for him, or why in particular DD-835 was named for him?

In general destroyers and other smaller surface combatants regularly got names of famous individuals related to the Navy or Marine Corps. As at the time Battleships took up the states, cruisers were cities, carriers generally famous battles or historic USN ship names, submarines were fish, leaving not much for all the rest.

For instance of just the Gearing class ships built at Bath Iron Works like the Cecil we have 7 named for admirals, 14 for Marines, and 9 for other navy men, women, or officials out of the 30 ships to come from that yard. It was extremely common for many senior officials and commanders to get a ship, especially decorated and deceased ones as Admiral Cecil was. Though short of digging through mundane minutes of meetings of Congressional Committees and Bureau of Ships meetings it might be a challenge to find why they came to this name for this hull.