Would they give me my package if I showed them my ID and the package has another name on it?

No

it would be best if u have a letter from the recipient stating that you are collecting in their behalf, even better with one of their id's and a letter post marked to them with their name and address

You have to bring a letter from the other person and a recent mail. It helps to bring a bill with the letter of consent

Your name has to be on the order to be picked up or you can have the recipient call and say they sending you to get the package