Image Size or Quality Issues After Batch Rename

When I go and rename a batch and place it in a new folder, it looks as if the image is saved smaller or with a lower quality. 

Batch rename only changes the filename. You can use Bridge to compare the pixel sizes before and after the rename.

I'm not sure what I'm doing wrong or how to properly batch rename. 

By @McKenzie37064695c2mm

Post screenshots and or type out before/after name examples to illustrate.