This happened to us with our Maclaren a couple years ago. There was a stroller identical to our parked right next to where we parked ours. Our stroller was not there. The stroller left had all kinds of tags on it with the people's names and their resort! I could not understand how they could have taken ours by mistake, which had no tags on it. Ours was in better shape, so maybe they were hoping to get a better stroller out of the deal.
Since their stroller was the same one, we assumed that they took it. We called the Poly where they were staying (according to the tags) and left a message for them that they had our stroller. We took theirs to Guest Relations. They got the message later that night and called us back and said they would leave our stroller at the front desk at the Poly. So we got it back, but it was a bit of an ordeal. The lady was not very nice about it. She was like, "well where did you put my stroller?" She was so annoyed that she was going to have to wait to have hers delivered to her later that day. No my problem lady!
So yes, from that point on we always put some sort of identification on our stroller.
Megan
*We also told a CM what happened and got a free rental for the rest of the day!*