Scenario:
There is a need for a user with only Project Resource-Billable permission profile enabled to approve expenses in an organization. When trying to add such a user as a specified user in the Approver Type, his user name is not displayed.

Cause:
This is because, the appropriate permissions for expense approvals are not enabled for a user with Project Resource-Billable permission. 

Resolution:
To resolve the issue, enable the permission entries Approval functions and Supervisor in the Approvals section under his permission profile.As the user is required to approve expenses, enable the permission entries Approve, Edit and View All under Expenses in the Approvals section.