If I have the full node on my hard drive and the node daemon running, is there anything else I have to configure to benefit the Monero network? Do I have to configure a domain name for others to connect / sync to it?
How does running a node benefit the network?
See the following:
Support the Network
Run a Node
An easy and effective way to help the Monero network is to run a node. Nodes ensure the network keeps running safe and decentralized. A simple fully synchronized node is enough to help the network, but if you want to go out of your way, you could run an open remote node, to allow other people to connect to it.
Do I have to configure a domain name for others to connect / sync to it?
No you do not need a domain name. However, if you want to allow other nodes to initiate connections to your node you will need to ensure your router / firewall forwards traffic to your host on port 18080. And if you want to allow remote wallets to use your node's RPC interface, you will also need to forward port 18081 to your host.