Question: What Is a Network Name?

Answer: A network name is a text string that devices use to reference a particular computer network. These strings are, strictly speaking, separate from the names of individual devices and the addresses they use to identify each other. Several different forms of network naming exist.

SSID

Wi-Fi networks support a type of network name called SSID. Wi-Fi access points and clients are each always assigned an SSID to help identify each other.

When a person speaks of wireless network names, they typically are referring to SSIDs.
See also - Changing the Default SSID on a Wi-Fi Router

Windows Workgroups and Domains

Microsoft Windows supports assigning PCs to named workgroups to facilitate peer-to-peer networking. Alternatively, Windows domains can be used to segregate PCs into named sub-networks. Both Windows workgroup and domain names are set separately from the names of each PC and also function independently from SSIDs.
See also - Naming Windows Workgroups and Domains

Clusters

Yet another distinct form of network naming is sometimes used to identify computer clusters. Most server operating systems, for example, such as Microsoft Windows Server support independent naming of clusters.

Network vs. DNS Names of Computers

It's fairly common in the IT world for people to refer to computer names as maintained in the Domain Name System (DNS) at "network names" even though they aren't technically names of networks.
For example, your PC may be named 'TEELA' and belong to a domain called 'a.b.com.' The DNS will know this computer as 'TEELA.a.b.com' and advertise that name to other devices.

Some people refer to this expanded DNS representation as the computer's network name.