re: is it important what I change the name to?
Nope, just unique.
re: and do I need to change both instances?
Yes, they must match.
re: I’ve changed the name and the new field appears in the users listing admin/edit area but does not show on the front end
Registering the custom field does not automagically cause it to display on the template. The reason is a custom field could represent any type of data or not to be displayed at all. To display it in the template, you need to follow the instructions at the bottom of the tutorial for displaying the text field.
I hope this helps!