If you want to delete everything from “_DSC” and to the right (but keep the extensions) I might suggest trying Find & Replace with a "regular expression."
1. Because there is no 'UNDO' in file renaming, you might want to consider applying a Metadata Template to the files and put {filenamebase} into an unused filed like "Supp Cat 1" That way if you accidentally do something to the filenames that you can't recover from, you would be able to rename the files at least back to their original state before you started fixing them. :-)
2. If you run Edit > Find and Replace with these settings, it will find "DSC_" and
everything after it and replace it with nothing -- but should leave the extension.
In the Find field: _DSC.*
In the replace field: Leave empty
Check the box for "Filename"
Check the box for "Grep" (When using Grep the .* roughly means "any number of characters")
Find and Replace works on items in the current Contact Sheet. You can choose to run it on all the items in the Contact Sheet OR to run it only on items you have selected. Keep that in mind. (Edited to add: Also, it looks like you have an extra space in all those filenames before _DSC. You can add that space in the "Find:" field if you want.)
"Regular expressions" (like .*) are used in programming and other apps, not just Photo Mechanic. They can get very (VERY) complex, so if you want to learn more about them you could get started here:
https://regexone.com/ but the basic use above should work without having to learn the whole regex system.
Go slow at first, and try with some small subset of files to make sure it is doing what you expect. I hope this helps.
Mick