I would beg to differ with the answers posted here, but Altium absolutely has the ability to do what you're trying to do.
Because people sometimes use different names than others for the same thing, I'm just going to show a basic example, not necessarily tailored to your question, but you should be able to modify this easily to suit your needs.
The key to the solution is the Smart Paste tool.
Lets say I have a bunch of ports and I'd like to paste them onto nets of the same name. Simply select and Copy.
Click Edit -> Smart Paste
Here I chose paste as net labels and wires:
The final result:
As you can see from the second image, you can paste as Ports, Net Labels, even as Sheet entries where you can paste them onto a hierarchy.
This is very useful for connecting say a connector block up to a new hierarchy with a large number of nets. For example, from the same original Copied material, I pasted this onto a sheet symbol.
I trust you can modify this to suit your original question.