There's always a way...
Rename all your apps with just a space, then no name will show up.
And, you have just a bunch of icons in your Applications folder (with no name)
(I didn't say it was a good answer, just an answer)
My neighbor kids come in and do random typing on my computer, so I get to remember the real names of the apps (not usually qwertyuiop[]\ )
some are simply blanked out, so the app icon in the dock now has no name, or whatever the 'new' name is now.
Not too practical, but there you are....
Even if you could do that (removing the text), how would you easily identify something that may not be usually kept in the Dock, such as a document, or an infrequently used app or utility?