From a little Web searching, it appears he’s probably something of a national hero. As a result, they named the sporting venue after him. Not really much different from Arthur Ashe Stadium and Louis Armstrong Stadium, part of the center where the US Open is held.
After a little googling, the name was picked because, besides being a war hero, Garros also was a member of the sport association that build the venue (the “Stade français”). Ha had won the french cycling championship in 1906 and was also a soccer and tennis player.