Directory Opus is working like that, and it's actually a very practical feature when you're dealing with a lot filenames you want to rename. Using the Up/Down Arrows works like saving the updated filename, and additionally it brings you to the next/previous file in your list.
An additional suggestion: it would make sense, should this "continous renaming" be implemented, to have the cursor land up on the "relevant" part of the filename you're coming to, based on the location within the name where you were. OK, for example: you're on file "This_is_123.jpg", and your cursor is right before "123". You're then using the Down Arrow to go to "This_is_456.jpg", and your cursor would be right before "456". Jeez, these things are difficult to explain
![Smile :-)](./images/smilies/icon_smile.gif)
Anyway, some sort of "continuous file renaming mode" would be a nice additional feature.