Classification with two 1-NN classifiers
There are multiple solutions:


Do linear scalarizing. E.g. If you have $d_0$ and $d_1$ then you could do:


$$D = w_1 d_1 + w_2 d_2$$


You could use the Pareto optimal front. The Pareto optimal front is the set of all distance pairs where one of the distances cannot be dominated without deteriorating the other one. This solution is probably not that well suited for your problem.
If you have a training set of linked object you could learn a model that predicts whether or not the objects are the same based on the distances. E.g. A logistic regression with the two distances as input. You could use a kernel or other non-linear tools to increase performance.


More ideas on this wiki about multi-objective optimization.