The computer name in this manner (it sounds like you are trying to use
NETBIOS which is handled by a WINS server) is not a reliable method of connecting to a server on a local network. What will happen is (if no WINS server is provided and no address in cache) the computer will send out
NETBIOS Name Query Request messages to the local subnet. If no response is received it then checks the
LMHOSTS file.  This is not the ideal way to set up a reliable FTP service to clients on your local area network. You don't give any detail on how your IP addresses or subnets are setup, so it may be that the clients aren't in the same subnet.
A dynamic IP is pretty much the main kicker when trying to run a server, especially for websites or FTP sites. In such a scenario, if the requests aren't returned based on your subnet, you would need to edit your
HOSTS file on each client to give the FTP server IP address a name like referenced here , which is not ideal because they would have to change this entry every time the dynamic IP address changes.
There is of course a way to setup virtual host names for FTP sites in your IIS version , but again, this would be of little use with a dynamic IP.
Long story short, for your clients to RELIABLY be able to connect your FTP server you should hardcode the IP address you want on the FTP box. Then you can setup your local DNS servers (if you have access to them) to resolve the name or you can edit the individual
HOSTS files on the client boxes and everything will be pristine.