Installing Teamcity build agent as a user: failed to install the service. selected account does not have enough rights

The error message says it does not have "enough rights to run as a service",
this is slightly different from just being an administrator.

1. Go to Control Panel> Administrative Tools> Local Security Policy.
2. Select Local Policies> User Rights Assignment.
3. Scroll down through the list of policies and look for Log on as a service.
4. Add the account you're using to the list of accounts with this right.

That should in theory be all you need to allow the service to run under that user.

The best powershell command that I have found for this is:

Grant-Privilege -Identity $SERVICE_USERNAME -Privilege SeServiceLogonRight

Requires use of the Carbon framework.