Currently I have a company that host a web based service for my customers, and we've agreed that the company would not have any branding of their own on the web site.
However they currently have their name on the web certificate, but we would like ours instead. Is there a way to purchase a web certificate for them to use with our name on it? The service is also accessed via an IP address and not a domain name.
You can't get a signed SSL certificate for an IP address. You can self-sign an SSL certificate, but it will give you a message when accessing the page. To get a signed SSL from a company like Verisign or GeoTrust, you'll have to use a domain name (and have a unique IP). You COULD get it to YOUR domain or get a wildcard that would also work on any subdomain of yours.