This sounds like a good idea/suggestion to be able to customize your own background. I've noticed everytime I refresh the page, a diff background shows up. Checked settings, doesn't seem to be an option to customize background. However, you could provide direct feedback to the hangouts team. In order to do so:
Please use the send feedback feature within Hangouts (clicking on the horizontal three-dots). This will directly send your suggestion straight to the hangouts team. The more feedback given about a certain feature, the more likely that feature will be implemented.