Internal DNS - FritzBox and Mac

On my Mac I connect to smb://192.168.1.123 which is a file server and from there choose the drive I want to mount. In Mac's Finder I see the IP address but I bet someone clever can give me a clue on how to set things up so I see the file server name, not IP address. And I'd connect to smb://FileServer (dot something?).

Somewhere in my FritsBox's DNS settings maybe?

A lot of ISP provided routers do not support internal DNS, but...
Try and see if there's a static IP setting within the router configuration and whether it permits you to set a "name" to go with it.

If it does, then it may support it. Set it up and then see if you can ping the name associated, from your Mac using a terminal.

This might be of help: https://en.avm.de/service/knowledge-base/dok/FRITZ-B...