Sorry about the issue. How are you trying to log into RStudio? Is this rstudio.cloud? or RStudio Server or Server Pro?
You refer to git, so do you maybe mean you're trying to set-up your credentials for git on your local machine, so you can use RStudio to commit and push changes?
The username for your login depends on the authentication provider and how its set up in Connect. I am unable to provide any guidance unless I have access to your configuration file. The best route here would be for your IT to work with our support team and get this sorted.