Pinging by hostname works fine for me. I can ping any device that has a hostname defined on the DHCP static page, using that hostname. I even access all my development routers by their hostname defined on that page, i.e.
http://rtac68:8080/ from within my LAN.
I had a similar problem and was scratching my head for a while. Here's what I've learned (all experience is based on .55).
Straight up: If you're using the merlin fw dns filtering for your client (or all clients) it appears (from my limited experience) by design ALL requests get forced to go to your chosen server - this server will not know your internal server names so they'll never be able to resolve "yourcomputer". Secondly, same rule applies if you went and added ANY OTHER DNS server (your ISP's, googles etc) to your clients either manually or to be handed out via DHCP. ONLY the router will resolve yourcomputer and ONLY if it handed that name out via DHCP (or your statically defined it and then manually assigned it on the client).
Beyond that, if you're like me and just configured everything up stock there's a couple of things:
Your "single label" computer name is a nonstandard form of address. To cope with this different OS's will use different methods to turn this back into an IP (netbios, dns, other) - resulting in weird shirt. eg nslookup being able to resolve your pc name but ping will not. Or more confusingly, a windows machine will resolve the name but OSX will not. I thought this was the router's fault, it's not.
This oddity results in you being able to do things like "browse to" windows servers but be unable to "ping" them.
The quick fix I have found is to get rid of the "single label" names such as "mycomputer" and define a bogus domain (eg my.lan) and hand this out via DHCP as the default domain search suffix (or manually configure if it you use static IP's).
Doing this forces all resolutions to go via DNS because when you try to go to "mycomputer" and the othre methods fail to resolve it, it will eventually get to DNS at which point it goes "mycomputer" is bogus, I will try mycomputer.my.lan and forward it to my dns server (the router) which will resolve it.
Edit: I said parental controls, I meant dns filtering.