machine name / computer name

hegedusa

In the article https://support.atera.com/hc/en-us/articles/231895308-Modify-agent-and-device-name

there is a section:

"Note:

 If the Agent Name and Machine Name do not match you must update the Agent Name to match the Machine Name before updating the Computer Name / Server Name on the machine itself. Both fields are case-sensitive. Learn how to modify the Agent Name"

What do they mean by machine name? Is this the same as Computer name/server name? Why do we need to do this anyway? What happens if (as is likely to happen) we do not remember to do this? Most of our agent names do not match the machine/computer/server name, so does this mean that we'll run into problems if one of us were to rename a computer, or if an end-user renames a computer?

I'm wondering if this is something to do with the search on the devices section not always returning the correct computers, even though I didn't rename any machines.