Anestis,
Your question is a valid one. It works down to this quesiton:
Do I really need a FQDN to have my BIM Server work?
My answer:
Well it could work without one. Take your chances, you have got a 90% chance that very soon somebody will complain about libraries showing offline. Your BIMcloud will work as designed if you only use ONE URL to access it. This one URL would be a FQDN. Not understanding the difference between 127.0.0.1, localhost, \\machinename, machinename.companyname.com, https:\\OurBIM.companyname.com in the end will hurt you.
That is, the people outside of your local area network are using a different URL to access the BIM Server than the URL that was used to share the project. For this reason the libraries are showing offline. You need to determine what the URL will be that accesses the BIM Server from everywhere. It will be something like BIMServer.yourcompany.com. Then set up your local DNS server to direct communication for BIMServer.yourcompany.com to 192.168.x.x (where ever you have the BIM Server) and your remote clients will access be directed to your router/Reverse Proxy/DNS sitting on your public IP address that is registered to "yourcompany.com". Once you have determined the FQDN for the BIM Server you will need to reshare the projects and make sure that the original entries in the client ArchiCADs for the old(bad) address for the BIM Server are removed.
In 19 this requirement has been relaxed.
Graphisoft Technical Support