There's two internationalization changes in play here. First of all, month names get translated. This is something that you cannot change without modifying core (as far as I know).
Actually what am I talking about. The obvious solution to this is to just create the page MediaWiki:January on your wiki (and the other months), editing the month names to whatever you want.
MediaWiki will use whatever is on the page MediaWiki:January as the word for January, which allows you to modify the output without editing mediawiki source code.
-bawolff