Make life easy for yourself and set your backups to use //ip_address/share.
The problem is caused by what is essentially an incompatability between linux (the OS on the DNS-323) and Windows and a very old Windows networking technology known as NetBEUI - Windows uses something called browselists to keep track of network shares, and the DNS-323 does not play very well with the technology.
There are several workarounds - one is to use a DNS server to translate the hostname to it's ip address, another is to use a host file on each Windows system - this is actually a "twist" on the DNS server work aorund mentioned above, but the easiest is to use the ip address as mentioned above.