Over the last century or so (1900 or so), there have been 1,764 named ships in the USN in the Destroyer/Destroyer Escort/Frigate lineage family; of which 1,342 names were unique.

Statistically, the 1,758 names that can be automatically classified break down as:

1,394 (79.02%): Last Names (i.e. Gearing)
118 (6.69%): First and Last Names (i.e Jonas Ingram)
5 (0.28%): First Initial, Middle Name and Last Name (i.e J. Richard Ward)
232 (13.15%): First, middle initial, and last names (i.e Allen M. Sumner)
7 (0.40%): First, middle, and last names only (i.e John Paul Jones)
2 (0.11%): First Initial, Middle Initial and Last Name (i.e S. P. Lee or W. S. Sims)

The top names (sorted by number of reuses and then alphabetically) are:

Decatur: 5
Truxtun: 5
Bainbridge: 4
Barry: 4
Cushing: 4
Dale: 4
Duncan: 4
Farragut: 4
Gridley: 4
Hull: 4
Ingraham: 4
Mahan: 4
Meredith: 4
O'Brien: 4
Porter: 4
Preble: 4
Preston: 4
Reid: 4
Sampson: 4
Somers: 4
Sterett: 4
Turner: 4
Worden: 4
Aaron Ward: 3
Aylwin: 3
Bagley: 3
Benham: 3
Buchanan: 3
Chauncey: 3
Conyngham: 3
Corry: 3
Davis: 3
Dewey: 3
Downes: 3
Evans: 3
Fanning: 3
Flusser: 3
Gwin: 3
Henley: 3
Hoel: 3
Jacob Jones: 3
Jarvis: 3
John Paul Jones: 3
Jouett: 3
Keppler: 3
Kidd: 3
Lamson: 3
Lansdale: 3
Lawrence: 3
Lloyd Thomas: 3
Luce: 3
MacDonough: 3
Maddox: 3
Mason: 3
Nicholas: 3
Nicholson: 3
O'Bannon: 3
Patterson: 3
Paul Hamilton: 3
Perkins: 3
Perry: 3
Reuben James: 3
Rowan: 3
Samuel B. Roberts: 3
Stewart: 3
Stockton: 3
Taylor: 3
Thorn: 3
Trippe: 3
Wadsworth: 3
Wainwright: 3
Walke: 3
Warrington: 3
Whipple: 3
Willard Keith: 3
William C. Lawe: 3
William M. Wood: 3
William R. Rush: 3
Williams: 3

The raw data for all 1,764 ship names is available (HERE) in a CSV file; while the stripped list of 1,342 unique names is (HERE) as a TXT file.

If you wish to use a random name generator to generate plausible Destroyer names (or personnel names) for wargames, I have compiled two lists for this purpose:

Anglo First Names List (CSV; Stripped TXT with only men) – 1,000 most common first names for men or women from the 1910 census (as their age would be 30~ by 1940.)

Anglo Last Names List (CSV; Stripped TXT) – 8,214 last names compiled from USN Destroyer Names, WITP:AE leader names, Forge of Freedom general names, and 5000 most common surnames.