How to reach local computer via machine name instead of IP?
Regardless whether you're connected to your local network via WiFi and DHCP is in use, Android always seems to override its DNS entries using Google's servers. It's somewhat hidden, but easy to change – provided you have your own DNS running (a lot of routers offer that already).

To do so, go to your list of WiFi networks in Settings, long-press your WiFi's entry, select to edit it. Activate Advanced Settings. Now you can edit the DNS entries. Simply replace the first entry with your own DNS server's IP, and leave the second entry (DNS 2) untouched for fall-back.

Now, if your own DNS can resolve your local network's machines, you should be able to use their hostnames to reach out to them. No root and no editing the hosts file necessary (thought that might be an alternative, if you've got no own DNS service running). Works excellent here with me and my network ;)