I was wondering if it could bbe possible to not show in the serverlist.

I have tried putting server.name "" in the server.cfg, but this sadly didn't seem work.

I was wondering if there's a way not to have it shown in the serverlist.

I don't know of any setting for this, but you could try contacting FP and ask them to blacklist you, although they will probably need some kind of proof of server ownership.

One way of getting unlisted is to disable EAC on your server, but you probably don't want to do this.

facepunch does have a guide for this https://wiki.facepunch.com/rust/Creating_a_hidden_whitelisted_server

the way the outline hiding your server from the server list is by blocking traffic to the queryport
which isnt something umod or a plugin can do afaik, thats something you have to do with your server hoster or server settings

Thanks I'll check the guide out

Make your server unsecure.