The MSDN documentation isn't precise on this point.
It says in one place: "Gets a collection of membership users where the user name contains the specified user name to match."
Later it says, "FindUsersByName returns a list of membership users where the user name matches the supplied usernameToMatch for the configured applicationName."
The SQLMembershipProvider supports wildcards, but the documentation doesn't say whether I must also do so with my custom membership provider.
Edit: I'm really asking more about the intent of the Membership Provider rather than what I should do in my specific situation.