Debian and GNOME have both recently adopted self-hosted GitLab for their git hosting. GNOME’s service is named simply https://gitlab.gnome.org/ ; Debian’s has the more intriguing name https://salsa.debian.org/ . If you ask the Salsa sysadmins, they’ll explain that they were in a Mexican restaurant when they needed to decide on a name!
There’s a useful under-documented feature I found. If you place a logo.png in the root of your repository, it will be automatically used as the default “avatar” for your project (in other words, the logo that shows up on the web page next to your project).
I first tried with a symlink to my app icon, but it didn’t work. I had to actually copy the icon.
The logo.png convention doesn’t seem to be supported at GitHub currently.