Basically, you can’t be sure. More of a problem with pets. When I had a pet cremated, they sent a video of the entire process up to and including them putting the ashes into the container. I was kind of like wtf? And they said I didn’t have to watch it, and they were happy to not give me the video, but that people were often concerned about just getting random ashes and that it was apparently common for some places to just cremate multiple pets and then dole out ashes to various containers, so they started videoing the entire process for each person so they could be assured they were getting their own pets ashes.

Seemed a little overboard to me, but I also didn’t realize it was happening so often.

There are much more stringent policies in place for human cremation, including the use of identification disks that don’t burn, etc. But, frankly, if someone wanted to, you could still end up with different or mixed remains, but I don’t really see that being likely for human remains.