It's absolutely still an F-15C. Far as I know, all that needs to be done is upload the new information (DLZ and special symbology) to the CC and that's that. No variant letter changes, no block number changes (Eagle block numbers aren't like F-16 block numbers...), it really is just 'some software'.
And no, it doesn't mean it's the Israeli version. We have a Fake Eagle, honestly. It's an APG-63 from 1978 with TWS, NCTR, and Slammer guidance...So why not throw some Pythons in there? Heck, put 'em on Flankers, too (PL-8).