Moving gmail messages in Mail to On My Mac folder naming problem

I am using Mail on the current version of Monterey to get my Gmail messages. I when I move them into the folder in the ON MY Mac section, all the messages show my name as the sender on the list. When I click on each message, they open with the correct information and the correct sender. I can search for a message and it shows up in the search results but the search result shows my name as the sender. I have to click on each result to see who the original sender was.

I am not forwarding these messages, I am either copying or moving them.

I just want to have a offline archive of my selected messages. Has anyone found a simple way to achieve this? I think what I described above is a bug in Mail at least in Monterey.