
For the team's first two seasons, their affiliation was split between the Celtics and the Charlotte Bobcats.

On June 21, 2012, the Red Claws announced that they had entered a hybrid affiliation with the Boston Celtics, making the Celtics the Red Claws' sole affiliate. This streak continued until the 2011–12 season, ending the streak at 48 consecutive games. During the 2009–10 season, the Red Claws were the only D-League team to sell out all 24 of their home games. The use of "Red" in the team's name also served to pay tribute to longtime Boston Celtics coach Red Auerbach.

The name and logo gave homage to the lobster fishing industry, a major economic engine of the New England area. On April 2, 2009, "Red Claws" was announced as the winning name after a name-the-team contest, beating out Beacons, Crushers, Destroyers, Swarm, and Traps. On July 21, 2009, the Red Claws announced Austin Ainge as the first head coach of the team.

On February 25, 2009, the NBA Development League (D-League) awarded the city of Portland, Maine, with an expansion franchise. The Maine Red Claws logo, used from 2009 to 2021
