As much as i love Kelly's writing, you gotta admit that stolen identity story arc is exactly that: a clusterfuck. It doesn't make much sense, and as far as i remember, it isn't even addressed in further volumes, with the sole exception of Cable & Deadpool.
For those of you who haven't been re-reading the first volume recently like i have, i'll help refreshen your memory. T-Ray brings back from the dead one Mercedes (supposedly) Wilson without her even knowing she's been dead for many years and sets her up to meet Deadpool, who recognises her as his late wife. We learn that Wilsons used to be a couple of happy tree-hugging teachers, until one winter day they pulled a barely alive stranger named 'Jack' from the river and decided to help him, only for him to lash out at them, kill Mercedes and leave 'Wade' for dead.
T-Ray gives them some time to reconnect and even start making plans, and then abducts them to tell his version of this story: that he is the real Wade Wilson, and Deadpool's 'Jack', who wanted to steal 'Wade's identity along with his wife's love in order to escape his employers whom he'd failed. But 'Jack' accidentally murdered Mercedes along with 'Wade' and went insane over that, while 'Wade' lived, trained to become a mercenary and eventually the abominable albino he is today.
All the evidence in relation to Deadpool's and T-Ray's real identities is listed here.
To me, neither version adds up. I've always thought that T-Ray is just bonkers, and he dragged Deadpool into this just so that he has someone to blame for what he's become, and because he's a sadisic motherfucker, too. He might've offed his poor wife himself for all we know, and contrived 'Jack' to distance himself from that crime. Any memories Deadpool shares with him and Mercedes could've easily been instilled, T-Ray is a powerful magician after all. That would add him to the long list of people who's tampered with Deadpool's mind.