IMPORTANT In order to rename a budget, you need to OWN the company (or have the proper manage rights), not "share" the company. Review that you are indeed the OWNER of the company first before renaming the budget 

You can quickly rename your budget by pressing the Rename button in the TOP MENU.

Enter the new name and press Submit.

Related Articles (Please refer to the links below) 

- How to SELECT a budget

- How to ADD a blank budget