You can recreate the current user's identity based on the InfoPath
username() function and pass the identity from there after a little string manipulation.
Even with claims based authentication this function will return you the current user's identity.
There is a nice blog post about passing a claims authenticated user's identity to the User Profile Service to retrieve profile information at InfoPath 2010 - Using the User Profile Service with Claims Based Authentication. You can follow the same steps to pass the identity to your WCF service. The author uses rules to achieve this, but you can also custom code this if rules don't do the job for you.
Also, see this SP-SE post: Why is GetUserProfileByName from InfoPath Forms Services with claims authentication failing?
Here the suggestion is made to use a
udcx:Authentication tag as a workaround.
Unfortunately though, I'd like to tell you Microsoft does not support InfoPath Forms Service with FBA. They state that fairly clearly on Plan for claims-based authentication or classic-mode authentication (SharePoint Server 2010):
Features that do not work with forms-based authentication or SAML security tokens
SharePoint Server 2010 Explorer View
Claims to Windows Token Service (C2WTS)
InfoPath Forms Services