Fpmurphy has created a Gnome Shell extension that allows you to add a logo next to the activities button and edit the activities button text.
Download the extension here.
Extract the file and place the extracted folder in the ~/.local/share/gnome-shell/extensions/ folder of your home folder.
Restart Gnome Shell by Pressing Alt + F2 and running r.
The extension defaults to show a Fedora icon. To change it to an Ubuntu icon, open the extension.js file and change “fedora-logo-icon” to “distributor-logo”.
Save the file and restart Gnome Shell.
To edit the Activities text, change the word “Activities” in the extension.js file to whatever word you wish to use. (I suggest adding 2 spaces before the word so it isn’t squished next to the icon on the panel.)
If you just want to use this extension to change the Activities text, and not have an icon, place “//” in front of “box.add_actor(logo);”
Or, you can place “//” in front of “box.add_actor(label);” to get rid of the Activities text and only show an icon.