What title is used for the player picked last in the NFL draft?

Mr. Irrelevant! Sadly for these last picks they usually do not even see the field before being cut from the team. There are a few rare exceptions. Tyrone McGriff was selected last in 1980 by the Pittsburgh Steelers and was actually selected for the 1980 NFL All-Rookie Team. Of course that was over 40 years ago... There is however one remarkable recent Mr. Irrelevant:

Brock Purdy, the 2022 designee, was propelled into the starting quarterback role for the San Francisco 49ers after injuries to the first- and second-string quarterbacks, Trey Lance and Jimmy Garoppolo. In his rookie season, Purdy became the only rookie quarterback to beat Tom Brady in a starting debut. Purdy became the first Mr. Irrelevant to complete a forward pass, a touchdown pass, and a rushing touchdown in the regular season.

https://en.wikipedia.org/wiki/Mr._Irrelevant

So I guess there is always hope...

Not every Mr. Irrelevant is irrelevant. Marty Moore, selected by the New England Patriots in 1994, helped the team to win Super Bowl XXXVI for the 2001 NFL season.

https://nesn.com/2010/03/mr-irrelevant-marty-moore-a-major-success-story-for-patriots/