Run an ls without getting the full path

(cd /other/directory && ls)

Is there some reason why you can not use ls -1 ?

$ ls -1 /other/directory
file1
file2

EDIT:

I notice you've changed the question now - my solution won't work with your new example of ls /other/directory/*.txt. Use something like khachik's solution instead, e.g.

$ (cd /other/directory && ls -1 *.txt)