@JR-BejeweledOne
Yes, it really depends on the nature of the function. In your case, you are attempting a bulk update to the datasource, so having the names completely match in the records is important to not having the function alter them as it goes. Not only would that slow it down, but also potentially cause some delegation issues.
To be honest, I sort of wished that they didn't support anything but the real names. I know that would make the app very confusing to "read" if you happened to have changed a column name, but to be honest, if I need to change a column name (other than Title), I usually delete the column and create a new one that is named the way that I want.
However, for functions that do support "renamed" names, you can also specify the real name itself. Example, if you rename an SP Title column to "Employee", you can use either of the following formulas:
LookUp(spList, ID=1, Employee) OR LookUp(spList, ID=1, Title)
They will both show the same results. The only real difference is that the "intellisense" in the formula editor will not show Title as an option.
You used to be able to turn this ability on and off in the app, but it seems that feature is long gone.