The default network config does request configuration from DHCP server for the interface.
If there is DHCP and DNS set up, the client (VM) would get all, including hostname.
There is hostnamectl to see/set name. However, the name that machine calls itself is not important. It is the other machines, where you use a name and need to get that resolved into IP address. DNS is the common way to handle the resolutions for whole networks.
So, the Synology should either have local config (e.g. /etc/hosts) to map a name to IP address of the VM, or get that mapping done by the DNS servers that it does use.
“Could not resolve host” in the VM? Like above, the VM has to first resolve the “httpbin.org” into IP address. If it has DNS configured, then it either fails to connect to that DNS server, or that server does not know that name.
nmcli should show most of current network config.
It is up to the Synology, how/if it offers “virtual” network between the VM and everything else.