In the long run, I believe the RStudio Cloud login will be the login to rule all RStudio logins.
There's already a connection to community, but I don't think it's in place yet for shinyapps.io, rpubs, or support.rstudio.com (support for pro customers), but that will eventually happen.
Also soon, you'll be able to update your email via rstudio.cloud profile settings, I think at https://rstudio.cloud/profile (so if you find this thread in the future, please check there for the option to update your email).
For now, to update your email on rstudio.cloud, shinyapps.io, etc., please email support@rstudio.com. There may be a couple of steps to verify emails, but we'll get you sorted there.