Over the last century or so (1900 or so), there have been 143 named ships in the USN named after states; of which (obviously) 50 names are unique.

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

North Carolina: 5 vessels
California: 4 vessels
Indiana: 4 vessels
Iowa: 4 vessels
Maine: 4 vessels
Massachusetts: 4 vessels
Mississippi: 4 vessels
Montana: 4 vessels
New Hampshire: 4 vessels
Ohio: 4 vessels
Pennsylvania: 4 vessels
South Dakota: 4 vessels
Virginia: 4 vessels
Washington: 4 vessels
Alabama: 3 vessels
Colorado: 3 vessels
Delaware: 3 vessels
Idaho: 3 vessels
Illinois: 3 vessels
Kentucky: 3 vessels
Louisiana: 3 vessels
Maryland: 3 vessels
Missouri: 3 vessels
New Jersey: 3 vessels
New York: 3 vessels
Tennessee: 3 vessels
Texas: 3 vessels
Vermont: 3 vessels
West Virginia: 3 vessels
Wisconsin: 3 vessels
Alaska: 2 vessels
Arizona: 2 vessels
Arkansas: 2 vessels
Connecticut: 2 vessels
Florida: 2 vessels
Georgia: 2 vessels
Hawaii: 2 vessels
Michigan: 2 vessels
Minnesota: 2 vessels
Nebraska: 2 vessels
Nevada: 2 vessels
New Mexico: 2 vessels
North Dakota: 2 vessels
Oklahoma: 2 vessels
Oregon: 2 vessels
Rhode Island: 2 vessels
South Carolina: 2 vessels
Utah: 2 vessels
Wyoming: 2 vessels
Kansas: 1 vessel

The raw data in CSV format used for the above analysis is (HERE).