Filter by process/PID in Wireshark

You could match the port numbers from wireshark up to port numbers from, say, netstat which will tell you the PID of a process listening on that port.

Use Microsoft Message Analyzer v1.4

Navigate to ProcessId from the field chooser.

Etw
-> EtwProviderMsg
--> EventRecord
---> Header
----> ProcessId

Right click and Add as Column

Just in case you are looking for an alternate way and the environment you use is Windows, Microsoft's Network Monitor 3.3 is a good choice. It has the process name column. You easily add it to a filter using the context menu and apply the filter.. As usual the GUI is very intuitive...

I don't see how. The PID doesn't make it onto the wire (generally speaking), plus Wireshark allows you to look at what's on the wire - potentially all machines which are communicating over the wire. Process IDs aren't unique across different machines, anyway.