Several of our users have asked us to include data relative to their account in the HTTP headers of requests we send them, or even responses they get from our API.
The header field name registry is defined in RFC3864, and there's nothing special with "X-".
As far as I can tell, there are no guidelines for private headers; in doubt, avoid them. Or have a look at the HTTP Extension Framework (RFC 2774).
It would be interesting to understand more of the use case; why can't the information be added to the message body?