You can use the Batch Rename function in Bridge to remove .xmp from your filenames. Beware that this is a powerful tool and you have to be careful to check the settings and the preview to be sure you will get the desired result or, more importantly, you will not make matters worse.
Select and image then right click.
Select Batch Rename from the menu.
In the New Filename section select String Substitution.
Find .jpg.xmp
Replace With .jpg
Check the preview at the bottom to confirm that the new filename is correct.
When you are ready to process several files, click the Preview button to see a list of how all the files will be changed. This is a critical step to make sure every file will be correct and no anomalies slip through

Note that the Destination Folder option allows you rename the current files where they are or make copies to a new folder, preserving the originals as a backup.
You should select "Preserve current filename in XMP metadata" as another precaution against unintended consequences.