Columbus Crew (first era)
Crew won their first MLS Cup in 2008.
Columbus Crew SC
The club rebranded to Columbus Crew SC on October 8, 2014, complete with a new logo. Winning the 2020 MLS Cup granted Crew SC the right to add a second star, which they placed above the previous one. 
On May 10, 2021, the Columbus Crew rebrands again, but as Columbus SC, or Columbus Soccer Club. This time it removes the "Crew" name, and replaces the circular badge with a wedge-shaped badge similar to the Ohio state flag, and with the letter C in the wedge. The 'C' represents the city of Columbus, and their fanbase which is nicknamed "The Crew".
Columbus Crew (second era)
One week later, after massive backlash from fans of Columbus and other MLS fans, the club released a statement saying that they've met with fans of the club and will reverse the decision to change the name, remaining as "Columbus Crew". The new logo remained but was altered to include the word 'Crew' and the number 96 representing their status as a founding member of the MLS.