Budgets can be changed by users with Budget Owner or Admin roles.
From the Budgets page:
Navigate to the desired budget. Hovering over fields in the budget line will reveal a pencil icon when the field is editable. Simply click into the field and edit as needed.
Look for the pencil icon.
You can also change the budget details by clicking on the budget name and changing the budget details within the pop-up sidebar. All fields are editable in the sidebar.
See also:
Budget Bulk Upload: Making Edits to Existing Budgets