I try to replace the former code-nodes with the new code-node and copy and past the script from an former code-node to the new code-node.
But this will not work.
There is no change in ‘File Name’ and ‘File Extension’ of the data-object.
Are you sure that code worked in the Function Node? Because honestly it does not look like it ever could have. Simple reason being that the keys have to be camelCase. So for example fileName.
This is the functionally workflow with old code-nodes.
How to use the new code-nodes?
Looks like you were in fact using camel case properties on your existing Rename File node @UweG 
So once you update your code accordingly, your existing code should continue to work as expected. I’ve tested this using the below example workflow on [email protected]:
This is the result:
Hope this helps!