Rest API to set member alias?

Summary

Can a member alias be updated via Groovy / Rest API?

Content

I have a request to allow users to change the alias of a member.  I was pretty sure it was possible.  I have a Groovy rule that picks up the new alias and it works fine for admins but it errors out for non-admin users.    The non-admin users get the following error: "...user has insufficient rights to perform the Save Member operation on the object..."

I'm having trouble finding information on Rest API that would allow me to do so.  Can this be done via Rest API? Does anyone knows how I accomplish this?  Thanks in advance for any feedback...