So I installed libreoffice 5.1, just to try and narrow down the problem. (I don't really like libreoffice so much, but for testing purposes...)
I found that the send to mail function works, and properly renders hebrew file names.

So that would indicate the problem is with Word, not with my email client.
I am using Affixa, it sends to Gmail (or other web-based email services).
But I had the very same problem with thunderbird, eMclient, and another one, I think mailbird. All of them, when receiving a command from Word, failed to properly render hebrew file names.

I have my windows system locale for non-unicode programs set to hebrew israel, so that's not the problem.

Any settings I can change in Word?