There was a very interesting interview with someone on the radio a few months ago (Radio 4, UK) who had written a book about primates.

He said that idea of a dog having a gender (i.e. distinct from its sex) was ridiculous. But he told us about his observations of chimps that were born female yet followed all the typical male-chimp behaviours, joined in male friendship groups, etc. It really sounded like a female chimp that identified as male, from what he said.

Difficult to really know what was going on since - as you say - they can't communicate with us.