Can you give some context or an example? "so-called" is well known. Ex: The so-called expert has a fake university degree. "so-named" is not familiar to me.

so named is occasionally used to refer back to something that has just been mentioned; for example: The Apollo space programme, so named by scientists in the mid-twentieth century, was at the heart of space travel. It does not express doubt. See the note from Chris (below) regarding so-called, which, as he says, is used when we want express doubt about a claim. hope that helps Helen