So far I only know about two bearers of this name. The inevitable wife - Ann, who is wife to William Henry Warner, and her father Thomas who was an ostler - hence the rather splendid drawing of a horse and a tree combined. I have not got any further, partly because of the ordinariness of the name (there are far too many Thomas Martins around to make a decision), plus the fact that, on the two census records I have, Thomas gives two different birthplaces - Kent and Hertfordshire.
Thomas Martin ca 1786-?
Derived from a christian name, which itself is said to be of Roman origin and associated with the god Mars - the god of war. St Martin of Tours is said to have inspired its popularity. However, there is also a theory that it comes from the Old Englsih Marton meaning a settlement by a lake (mere). So therefore a place name.
Martyn, Marton, Marten, Martini etc. in many different languages
In 1891 the Martins were split between Yorkshire and Lancashire in the north, with an outpost in Staffordshire, and Devon and Cornwall in the south-west, as well as virtually all the south-eastern counties. The Midlands miss out a bit.