If you have joined someone else's group album and are not the creator, you may not have permission to change the name of a group album. If you are the creator, however, follow these steps to change your group album's name:
MOBILE: After you are in the specific group album you are trying to change the name of, tap the "Settings" icon (this is a gear/cog on iPhone, and an icon with settings sliders on Android) and you can change the group album's name in the editable "Name" text box provided.
WEB: Go to the "Settings" tab below your cover banner at the top of the specific group album you are trying to change the name of. Under "Name This Group Album" if you click directly on the current name of your group album you should be able to edit the text directly.
Just wanted to add, In order to set the new group name, one must click the "enter" or "return" key as this will post a popup verifying that the group name has been updated or changed. For the longest time, I couldn't figure out why my group name wasn't saving until I clicked the enter key.