In your case, if your question is how to 'mark' incoming mail that has been forwarded to your Gmail inbox, you need to do the following:
In your email@example.com inbox, go to the gear in the top right corner and select settings. Then you need to go to Filters and select Create new Filter at the bottom.
In the next menu, in the To field, you must specify the forwarding address (firstname.lastname@example.org).
This will automatically mark all mails forwarded to you from the specified address.
Refer to the screenshot:
I have erased the bigger parts of the domain in the picture to avoid spam. So in this case we work with 2 email addresses:
Note, there is a 3rd email address present. We will call this email@example.com.
So the scenario looks like this:
rudolph@orig is set to forward all mail to firstname.lastname@example.org. In the screenshot, I've sent an email from rudolph@sno to rudolph@orig.
Therefore in my email@example.com inbox, I've set all mails TO: rudolph@orig will be labeled and placed in a folder.