Can I keep my backpack with me on train

Anything you want, as long as it doesn't take up another seat, and even then it wouldn't be a problem unless the train is pretty full.

Thanks Sam! That is what I figured. Go Pack!

I have traveled extensively in Europe on trains. It's safe to put baggage in the overhead. A good idea is to put it in the overhead opposite your seat. That way, you can keep an eye on it. If you put baggage at your feet, it could cause clutter for other passengers in the compartment. If you feel safer, put your baggage on the seat next to you, but you might have to move it for another person.

If you go to the restroom on the train, it might be a good idea to take your baggage with you, though it's cumbersome. Better still, go to the restroom in the train station before getting on the train.

Have a great trip to Italy! Cheers.

You can be as uncomfortable as you want on the train, it is not like a plane. Would be inconsiderate to put on an empty seat next to you unless train is nearly empty but otherwise no issues with keeping on your lap or on your back and sitting hunched over.
I travel with my expensive camera and lens (plural) inside my backpack so it never leaves me. I usually placed between my legs on trains and wrapped a strap around my leg so no way to grab it without taking me along for the ride.

No way I am leaving 5 grand worth of gear in any compartments in a train or bus.
The issue with a backpack though is they are not allowed for many sites. I brought along a messenger bag for me to carry the camera and one extra lens on most days as I feared I would be denied entry with my backpack.

Thanks Craig!

Thanks mreynolds! I have a small messenger bag as well. The backpack will stay in my room once I reach each new destination.

One more idea: Sometimes people lock their baggage to the overhead racks with a combination or key lock. Loop it around a strap and a rack. I've never done that but have seen it.

On some trains there is an A-shape space between the back-to-back seats. I usually put my carryon there, in the space across the aisle, so I can see it, rather than behind my seat.

The overhead rack is very safe. Who's going to take your bag with you sitting below?

I can see the risk only if you go to the bathroom. In that case, it's a good idea to have a cable lock to secure it to the rack. The overhead rack will accommodate suitcases the size of a carry on or even a bit larger. At the ends of each car there are luggage closets for the large suitcases. I don't know if you will need that, but if you do, make sure you lock it with a cable lock, since those won't be within watching distance from you seat.

The possibility of pickpockets or thieves on high speed Freccia trains is near zero. They are too expensive and not crowded enough for thieves to invest on a ticket. Your luggage will be safe there even if you go to the bathroom. The risk exists on cheap but sometime crowded regional trains, which serve commuters, and of course, equally crowded subway trains and city buses. If you can, avoid using crowded city buses and subways. 90% of pickpockets happen there. Use a taxi or walk, especially when you have luggage with you.

On the rack, never on a seat. Taking up two seats makes a very rude impression.
And there is no reason to be afraid something happening to it when visiting the toilet. In the sight of everybody in the carriage? It is not usual to ask a passenger next to you to keep an eye on your belongings when you're away for a few minutes.

For train travel I put my suitcase in the overhead--locked--and keep my tote bag and purse at my seat--I travel solo so depending on the length of the journey and other factors I sometimes take my tote bag into the restroom with me, sometimes it goes in the overhead.

On trains I haven't had problems putting my Euro tote bag or Civita backpack under my seat; overhead storage also works. Roller bags go in the A-space between seats, if possible, or at the end of the car-- but it took several trips to develop that level of trust in the train system. Since there are two of us, we take turns going to the restroom so there's always someone sitting with the smaller bags.

Thanks everyone!

Well, I got to 53 years living in Italy and I would say that the only time I saw a large piece of luggage being stolen, it was in Chile. Pay attention to wallets and handbags, instead.