When you run a simple mantel test, do the distance matrices have to be in the same order and to correspond the rows to the same individual or register?
Not sure I fully understand your question, but almost all spatial analysis is going to require that you keep track CONSISTENTLY of the entities. So I'd say yes, you need to preserve the ordering. In fact, one of the ways that we might do a simple simulation test, would be to compute for the OBSERVED labels, and then scramble them (say reorder them 100 times) and see how DIFFERENT the observed value is from the distribution of values from the variations? Maybe this does not make sense from my poor explanation, but take a look at a book like EXPLORATORY SPATIAL DATA ANALYSIS by Bailey and Gatrell. I think it does a good job on the idea of simulating random variations on the observed data.
The simple and partial Mantel tests are routinely used to assess the significance of the association between two or more matrices of distances relative to the same pairs of individuals.
A free and friendly program to test their hypotheses of association is the ZT program (Bonnet & Van de Peer 2002).