First time Rocket owner looking for simple advice on oil changes

Using,
Bel-Ray EXS Full Synthetic Ester 4T Engine Oil last 2 oil changes seems good.

Also 4T oil has Zink in it to help protect the valves and seats.
 
WELCOME to ya, Comotion from WA State.
Mobil 1 Racing 4T 10W40 (Case - 6 Quarts)
 

The filter your describing sounds like a K&N chrome filter. They have the nut on them for easy removal. The hole is for safety wire if you race the bike.
 
Welcome Comotion

Someone soon will come along to advise on the filter questions. You will most likely get a few choices for oil brand a weights.

Where in the States are you located? Different riding temps will determine the oil weight.

Thank you! I'm in East Tennessee, and while it's not always warm in the winter, we ride year round.
 
Thanks to everyone for the quick and detailed responses! Based on this info, it does look like an aftermarket filter. I should have posted this photo to start with:
 
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I'll be leaning on y'all a lot. I went to the local Triumph dealer and asked the service tech about the chrome filter cover, and he said he had no idea what I was talking about. That didn't give me a warm fuzzy feeling about the dealership.