No, this is not possible. We have the one way of creating the site, described below. Some customers send suppliers to sites that are suppliers.companyname.com and from there they can access the site.
"http://customername.sourcing.ariba.com where customer name can be anything, but the domain part can’t be changed."
There might even be issues with customers creating an alias of say companynamesourcing.com but that actually sends them to companyname.sourcing.aria.com.
David