[mothered]

No, they just make sure its you and thats it

That's good.

As far as you're concerned, someone else picked up the package (not yourself), hence It comes down to human error on their end, by providing the package to the wrong person. They have no record to cross-check details. Have a look whether there's CCTV cameras In place, though.

I don't have any ID for the fake name tho

No, you use your real ID and then a couple of days later, go back to pick It up.

Obviously It won't be there (you've already picked It up), therefore as far as you're concerned, they've given It to the wrong person. On the grounds they do not keep a copy of IDs, they cannot cross-check any details.