Your question doesn't specify where on the network you are capturing packets or what type of network, but I am going to assume from a regular computer on the network. If you are running Wireshark on your computer, you will typically only see traffic addressed to your network interface (unicast, multicast, or broadcast), unless you are somehow using a hub instead of a switch. This is either due to how switched networks work, or the way wireless cards work in managed mode.
In order to monitor the entire network, you have a few options:
- Run the packet capture from the gateway router so that all traffic to and from the network will be captured.
- Force other devices to send their traffic through another computer that performs the capture, perhaps using ARP spoofing.
- Configure all devices to use a proxy; perform logging/packet capture on the proxy.
- Sniff the wireless traffic using a wireless card in monitor mode.
David's answer points out some of the ways you could look for the domain name. An additional point is that HTTPS is also possible, since TLS traffic typically has a SNI header containing the domain name (unless the encrypted SNI extension is being used).