You can adjust the order in which the columns appear in the register view.
To do this, simply navigate to the template register view & select Edit Columns (in the top, right-hand side). This will open the column settings where you can:
Select/un-select fields using the checkboxes to hide/show them in the register view
Drag and drop fields to rearrange them in the register view
Notes:
Only users with Team Controller permissions (and above) can edit column settings. These changes will affect everyone who views the register, not only for your account.
By default, each template will have Standard Columns - capturing:
Project
Team
Created By
Created Date
Last Updated
Form ID
Form Version