I had a similar issue in Kali Linux and found the solution here:
https://forums.kali.org/showthread.php?33063-Application-Menu-Width-Issues
The author expressed his suspicion that there must be a better solution but it worked for me like a charm. No more guessing what the menu item does!
The essence of the answer is here:
Edit this file (may require root privilege):
/usr/share/gnome-shell/extensions/apps-menu@gnome-shell-extensions.gcampax.github.com/extension.js
Look for...
this.categoriesBox.box.width = 300;
(just search for 300)
...and replace it with:
this.mainBox.box.width = 950;
this.categoriesBox.box.width = 500;
Save, logout, and log back in. Should be much better.
If not, play around with those numbers. Main box is the width of the entire menu; categories box is obviously the size of the categories box within the main box.