While rarely used, Tasman has a fantastic namesake in the Dutch explorer from the 1600's Abel Tasman. The Tasman Sea is named for him; plus two marsupial species (albeit indirectly - the Tasmanian Devil and the Tasmanian Tiger); an island state in Australia (Tasmania); a bridge, highway and peninsula in Australia; and a glacier, lake, river, bay, mountain, district and National Park in New Zealand all bear this name.
It's a masculine sounding name, with the cool, masculine sounding nickname of Taz. It also has the popular -an ending sound. Tasman has English origins, meaning "of great faith". Yet it seems to remain relatively undiscovered, other than making the rare appearance on forums in the form of people who know one or have met one.
So is it the crazy image on the Warner Bros character the Tazzie Devil that is keeping his name out of the consciousness of baby namers? Or is is just that people outside Australia and NZ have hardly heard of it, while people in those countries hear it too much? No matter what it is, I think this is one name that has the makings of a popular name in the future.