Sixteen teams are named after persons or groups of people.
Three of these peoples are seaborne outlaws: Vikings; Buccaneers; Raiders. Three are named after particular jobs: Cowboys; Packers; Steelers. Two are named after American Indians: Redskins; Chiefs. Two are monsters from mythology: Titans; Giants. Two are named after individuals: Browns (after Paul Brown); Bills (after Buffalo Bill Cody, by way of a famous barbershop quartet?). The others are in no particular sub-category: Texans; Saints; Patriots; 49ers.
Nine teams are named after mammals.
Four of these are felines: Bengals; Lions; Panthers; Jaguars. Two are equines: Colts; Broncos. Three are in no particular sub-category: Bears; Dolphins; Rams.
No less than five NFL teams are named after birds.
The five birds are: Ravens; Falcons; Eagles; Cardinals; Seahawks.
So most NFL teams are named after living things, most of them aggressive. The five bird teams form an interesting cluster of names, particularly since three of the four finalists for the Championship this year were birds.
One minor category remains.
Two teams have names derived from science/technology: Jets; Chargers.