Thanks for your continued response. I guess I would like to ask 1 more question, and contribute my findings.
Question: What is the condition "Name" with attribute "Did Change" used for? What is a use case where is would match rule?

Findings: I could not get any data point or date to change when changing a name.
I named a file FilenameTest123.txt on 1.59pm
Then I renamed it in the finder at 2.04pm.
There are no indications at the Hazel Preview that anything has changed, so of course, assuming the the rule doesn't match.
upload imagesBased on this, I think I get it... Hazel captures the date of the last time it checked a file and it's basic attributes?
So, I guess, would it make more sense to use Date Last Modified is after Date Last Matched 'because' it uses the last time hazel compared the file in Hazels' database it the file itself?
With that in mind, is there a way that we can see how Hazel sees the file, rather then how the finder does?