I have a VSTS instance that is backed by an Azure Directory. This is a great way to help secure a VSTS instance, only users in the Azure Directory can be added to VSTS, not just any old MSA (LiveIDs). This is a directory that can be shared with any other Azure based services such as O365, and centrally managed and linked to an on-premises Active Directory.
When I tried to add a user to VSTS, one that was a valid user in the Azure Directory, their account did not appear in the available users drop down.
Turns out the problem was who I was logged in as. As yo can see from the screenshot I have three Richard accounts in the VSTS instance (and Azure Directory), a couple of MSAs and a guest work account from another Azure Directory. I was logged in as the guest work account.
All three IDs as administrators in VSTS, but it turned out I needed to be logged in as the MSA that owned the Azure subscription contains the Azure Directory. As soon as I used this account the dropdown populated as expected and I could add the users from the Azure Diretcory