Wade Wilson was born as a normal person into a highly dysfunctional family in a small town in the state of Ohio. He ran away as a teenager and bounced around the country, all the while getting military training from various sources until he decided to become a mercenary. He kept changing his identity whenever something went wrong with the mission. He moved to Canada where he met a man by the name of Wade T. Wilson. Since he was Wade W. Wilson, the name reminded him of his old self. When he was ordered to assassinate Wade T., he accidentally killed the target’s wife, Mercedes. In the end, Wade T. ran away to eventually become the voodoo mercenary T-Ray while Wade W. kept the name “Wade T. Wilson” and never changed it out of respect for his namesake’s wife. When he was diagnosed with inoperable brain cancer, he volunteered for a subset of the Weapon-X program that was attempting to imbue a normal human with Wolverine’s healing factor.
Since he is Wade T. Wilson, he has Canadian citizenship, allowing him entry into the Weapon X program. The procedure was a success, but Deadpool, who took his name from the pool that the officers and scientists bet in as to who would die next in the experimentation, became severely mentally unbalanced as a result of it. He escaped the facility and has been wandering ever since. Some people might speculate that before his name was Wade Winston Wilson his name was Jack though this isn’t confirmed.