You don't necessarily need a gmail account. I was able to change my google background with my youtube account. If you have a youtube account, try logging into google with the email address and password you use for your youtube account. If it doesn't work...well I don't remember how I did it. XD
By the way, if you post a picture of your background here and don't want people knowing your email address, make sure to blur or cut out the area where it appears.