If you want a sophisticated or permanent solution, Bonjour protocol may fit, you can see its implementation in Linux Avahi. So you can point to your NAS as hostname.local or use Avahi Discover to get IP's and all services published in the network. (printers, ftp, smb, ssh...)
Minimum installation for client side (your machine):
sudo apt-get install avahi-daemon avahi-dnsconfd avahi-discover avahi-utils
avahi-dnsconfd listens to the publishing and passes them to resolvconf. So you can point to the server as
nashostname.local. as any other real public domain name. You can use it with http (firefox), samba share, ftp,...
$ ping salah-Aspire-5738.local
PING salah-Aspire-5738.local (192.168.1.3) 56(84) bytes of data.
64 bytes from salah-Aspire-5738.local (192.168.1.3): icmp_seq=1 ttl=64 time=6.09 ms
$ nmap salah-Aspire-5738.local
Starting Nmap 6.40 ( http://nmap.org ) at 2014-01-30 15:31 CET
Nmap scan report for salah-Aspire-5738.local (192.168.1.3)
Host is up (0.066s latency).
All 1000 scanned ports on salah-Aspire-5738.local (192.168.1.3) are closed
Nmap done: 1 IP address (1 host up) scanned in 4.91 seconds
avahi-utils, GUI & CLI, are the user interact tool. They are optional in case you want to list all services published on the network.
Avahi Discover showcase
For NAS server side, if it is a Ubuntu base (Linux/BSD you can build source):
sudo apt-get install avahi-daemon
avahi-daemon provide services publishing.
In case you are using Commercial NAS, many of them support service publishing using Bonjour.
See Avahi (Wikipedia) or its official website.