It`s always best to rename the file before commencing the download. However, the file to be renamed is MBAM.
You can also rename the MBAM shortcut on your desktop - providing you saved the installer to that location? And yes, just right-click and select rename.
When you use the "Save as" option before downloading - that is when you can rename it.
Help with Malwarebytes is available at their forum: http://forums.malwarebytes.org//
If it's already downloaded then there is no need to rename assuming it is working OK, if not ask on their forum.