When I inspect the logo in Chrome, I can see it is coming from :
http://RA-SERVER:8080/datamanagement/images/5cabcd2a.logo_grey.png (this is on v6.2)
This is based on the css class="logo".
I will advise that replacing this image with your own will work, but will revert back to the stock image after each upgrade, including minor releases. It is also possible that the file name could change between releases. If you're OK updating this every time you update Release Automation, then you're good to go.
I did something similar - I adjusted the background color for the DEV instance of RA, so you would always know you are in DEV vs PROD. However, I got tired of trying to find the right image file to replace every upgrade, so now DEV looks just like PROD. Oh well...