Yes. To modify the categories list, click on the Pencil & Paper (edit) icon categories next to the Categories label from any constituent profile page.  

In the new window you can edit any of the existing choices by clicking on the Pencil & Paper (edit) icon to the right of the item. Click the Disk (save) icon on the row to save your changes. If an item is not in use, you can delete it by clicking on the Trash Can icon.  You can only delete a choice if it is not already in use.

You can also make categories Public or Private by clicking on the Lock icon. If you utilize the memberships directories, they are searchable by the categories. So if you prefer to have some categories hidden from public view, click the Lock icon and ensure the lock is Red. Green locks are publicly visible categories. Click the Save icon to save your changes.

Click Close to see the edited list choices available. 

If you want to delete a choice that is in use, you will need to identify all the constituents using that choice. You could filter the Constituents Grid to identify the constituents and use the Batch Update feature in the Actions menu to remove all constituents from that category.