All baggage on Amtrak is supposed to have name tags, with the owner's name and some sort of contact info (address, cell #, or some other way of contacting the owner.)
This is enforced for checked luggage and if an Amtrak employee notices a carry-on is not tagged, they will ask you to put a tag on it, but I don't know if they insist or just recommend it.
If you both had tags, it is much less likely that either of you would have grabbed the wrong bag and if you did, it would be relatively easy to get it back. Of course, if one of you is in the middle of a long trip and is still away from home, it could take a while.
Most likely the person who took your bag did so by mistake and is just as desperate to get their own bag back as you are.
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When I bought my big LL Bean wheelie duffel bag and had to pick a color, I chose a bright yellow one, thinking it would be easy to spot on an airline baggage carousel. The first time I took it on a plane, one of the first bags to arrive was an identical yellow LL Bean large wheelie duffel! Fortunately, I had bought mine with an LL Bean credit card and got the free embroidered initials on it. (It also had a luggage tag, of course.) But the dead giveaway was mine had previously survived a couple of camping trips and was filthy. For second, I thought TSA had washed my bag for me, but no such luck.