From Muppet Wiki

Captain Flint is the fabled buccaneer captain in Muppet Treasure Island. Flint is glimpsed in the film's prologue, bringing his treasure ashore to be buried, and ruthlessly shooting a shipmate to preserve the secret.

Though long dead during the film's main narrative, the search for Flint's treasure drives the plot. It was also Flint who callously took up with Benjamina Gunn, after she was jilted by Captain Abraham Smollett, and stranded her on the island.

His first name is Bernie.