Sometimes messages from the Matrix side come across with the generic bridge app as the user's avatar.

I have talked it through with @Half-Shot and he says:

I think it's something about how we cache all member state in the bridge, except I think that cache has holes in it

As a workaround, you can change your display name in the Matrix room temporarily (/myroomnick ... in Riot), send a message, change it back, and things work as expected from that point on.