How to access restored iPhone 5 with new apple ID?

About 6 months ago, I went to fix an old iPhone 5 to a computer repair shop, it took a couple of weeks for me to get my phone back because they never called and I always forgot to call them to see what was going on. It sounds so irresponsible but I didn't actually need the phone, I just wanted to get it fixed so I could give it to a family member that needed it but we had no hurry so I always forgot. ANYWAYS, after some weeks, I went back to the shop and found out they had moved to a new location and with the hectic move they forgot to call. They gave me "my phone" without a charge and told me they couldn't fix it. I went home a little disappointed. I've had this phone for months just laying around the house and never threw it away. Today, out of curiosity I turned it on and the "connect to itunes" message popped up. I got so excited. It gave me the option to update or restore so I chose to update it. Then it asked me for my passcode, I enter it and it tells me it incorrect. I reconnected to itunes and a message pops up telling me if I want this computer to access the information on "KTs iPhone?" but my name is not KT. I instantly realize the guy gave me the wrong phone. I restore it and use my current phones sim card bc it had none but it won't let me sign in with my apple ID. It wants KTs apple ID. Is there anyway I can use my apple ID instead of KTs?

Not possible

No. If you don't get your phone back then the phone you have is of use only to the real owner.

If you leave your stuff uncollected at places like repair shops, dry cleaners and similar places then most have conditions which state they may dispose of uncollected goods. If so then you have no claim against the shop. But it's possible that KT may have your phone, so it may be worth trying to contact KT by handing in the phone at an Apple Store with a message for KT to contact you. Even if KT hasn't got your phone, there may be insurance on the phone you have which pays a modest finder's fee.

The shop does seem to have acted unfairly, incompetently and possibly dishonestly though, so it may be worth reporting them to police in case they're dealing in stolen phones, and also to any local consumer protection organisations; in the UK that could be the council Trading Standards department. Your individual complaints might not result in any action by themselves, but if there have been other complaints or are subsequent ones about the same shop then it might result in an investigation which could stop others losing their stuff.