The Strong Authentication Expert Group in the Liberty Alliance is, amongst other work, defining enhancements to the normal interaction between a Service Provider (SP) and an Identity Provider (IDP) as spec'd out in SAML 2.0 - these to better support strong authentication to the IDP (and, importantly, an ability for the IDP to accurately describe such authentication to the SP).
So, what to call this sort of IDP?
As the new functionality is quantitative rather than qualitative, 'merely' a new layer on top, the 'marketing' answer to the question is clear. We need a name that suggests the exact opposite, i.e. that this sort of IDP is nothing like the old type, a name that sends the message 'New and Improved!', 'Gets Whites Brighter', 'Low on Carbs', etc.
We need a name that even suggests these new type of IDPs won't even work with old-style SPs, this is no dot-release for which we can guarantee backwards compatibility.
If only there were an example of such branding in the identity-space to guide us.
Perhaps just change the emphasis of the letters of the spoken acronym to distinguish old and new, as in 'ShinaGAWA' and 'ShiNAGawa'.