There's already a test that does:

    RestAPI.Tenants.updateTenant(globalAdminRestContext, TestsUtil.generateRandomText(), {'displayName': 'I\'m totally legit...'}, function(err) {
        assert.ok(err);
        assert.equal(err.code, 404);
    
        return callback();
    });

I had just glanced at the `updateTenant` function and thought it could change the alias, but I see now that it's using it for lookup.