Searching by Name

Looking for insight or recommendations or experiences with the following:

A client has SQL based web application that searches multiple databases on
different systems on many fields but in particular: NAME

Issue: User is looking for a person named "Joe", they type Joe into the
search and don't get the full results because databases are storing the
name as "Joseph". Same thing with Nikki and Nicole.

Obviously, we can use SQL wildcards % and LIKE so you could search by "Jo%"
or "Ni%" but users may not do that. I've started to analyze FULL TEXT
searches. Anyone already been down this road?

Thanks, Paul Holm