Is there a way to batch copy port names over to net names
You can use the Edit > Smart Paste function.


Select all your ports, 
copy them (Ctrl+C) then use 
Edit->Smart Paste and 
select "Net Labels" in the dialogue. 


Then Altium Designer will paste net labels with the same names for you.
This also works for Power Objects and busses. Take a look at the options in the dialogue or the documentation for Smart Paste.