I should provide some additional information on my problem.

I realize now that the Worksheet level version doesn't do anything
because the names I am trying to erase are Workbook level.

When running the workbook version I get a run-time error. The error
is a 1004 run-time error that says, specifically, "Method 'Range' of
object '_Global' failed."

When I press the "Debug" option it highlights the following part of
Gary's code:

If Not Intersect(Selection, Range(rngname)) Is Nothing Then

If I use the exact same code on a new workbook created to test it, it
works as intended and erases the range names located within the
selected area.

I have ensured none of the worksheets nor the workbook are locked in
any way. I have also unlocked all cells to see if that would do the
trick, no luck either. I don't know what else to try.