There are so many names for this tune. The Little Beggerman has words that are quite common. My friend John's dad used to call it The Old Soldier With The Wooden Leg. He sang:

There was an old soldier and he had a wooden leg
And he had no tobacco so tobacco he would beg...

A version from Newfoundland called The Old Ragadoo goes:

I'm a hearty Newfoundlander; Michael Chaser is my name.
I was born on Green Island I'm a fisherman by trade
I was born on Green Island 'bout a quarter after two
With my hands in the pockets of my old ragadoo...