[Rare Justice Emperor]

I’m sorry English is not my first language, but I didn’t give them an ID yet. I just signed the document under a false name and signature and they’re asking for the ID. I was thinking of telling them that I don’t have an ID because it was stolen but that would be too obvious.
I still have the original return document because I generated one online, so I could still return it but I don’t know how that will affect me or if there will be repercussions…

how come you sign a false name when the claim is yours ... try to repeat the steps as legal documents are expected outcome on such regular claims so this time enter everything right if available , you could've ended up refunded as such legal document's are so normal demand from companies when doing such claims as i said .
on the ID part just replace similar numbers with each other , also check the type of the legal document but in most cases they are just used internally within the institution to proceed up with claims .

Because I'm stupid, I really hate myself for this and not going on sinisterly sooner. Should I just tell them that I used a wrong name by accident? Or just send it back... but I'm worried I'll get in trouble with the law.
Thank you so much for your help, though. I really appreciate it.

no your not stupid and don't hate your self as mistakes happens from all of us at some point .
just say your friend filled the papers when you were absent not knowing what he did and upon informing you that you decided to make it right as the person who filled the legal document was not you .

if you are insisting on the "legit" return i've to tell you its very hard in your situation as your intentions were clear by sending an empty box/envelop using "ftid" method , if it was EB/DNA claim coming up with an excuse will be much easier .

EDIT : since item weight is too low i don't even think they may notice anything as you literally boxed the return . so you should be fine , don't worry and stick with your story ! you did a legit return and it's not your fault as you sent back what they needed .