The 'Name' field can be used to identify different nodes when accessing the nodes with python.
I might have 2 diffuse type nodes, 'Diffuse BSDF' and 'Diffuse BSDF.001' and be able to identify which node I want to change a property on, by it's name:
This would access the
use_custom_color property on the node called "Diffuse BSDF".
I know which node I am accessing by looking at the 'Name' field in the node editor.
Because I am accessing the nodes by name, it might be useful for them to have more descriptive names to help me separate them from other nodes e.g. "diffuseMain", "diffuseOriginal' etc. I can use that name field to rename them to something more relevant and identifying.