Tortuga (trans. Turtle) is an Island off Haiti, apparently named by Columbus’ sailors in 1494, was a centre of piracy in the 17th century. It featured as a location in the Pirates of the Caribbean films (see below) which was the inspiration for this name according to a former resident. The flat was renamed after their Shrieking Shack sign was stolen earlier in 2015.
Here’s the Tortuga scene from Pirates of the Caribbean.