The trio have all put pen to paper on one-year deals at the Crown Ground.
Striker Carver made his debut as a second-half substitute at Bristol Rovers last weekend where midfielder Stockdale travelled down with the matchday squad.
Hopper, also a midfielder, has featured four times for the first team since Paul Cook replaced John Coleman as manager in February.
"It's very exciting to sign my first professional contract," Hopper told Accrington's official website. "We've been talking about it but it's great to actually get it done and I just want to kick on now. Next year is a chance to show everyone what we are all about."
Stockdale added: "I just want to get out there and show what I can do. If I get my opportunity on Saturday then great, if it comes next season then I'll be ready. I just need to keep myself ticking over the summer and give myself the best possible opportunity in pre-season."