For an example of how to conduct a multidimensional project in isonymy, have a look at the Irish Isonymy Project of Don MacRaild and Malcolm Smith. The main focus of the project is the use of random isonymy to track 19th century Irish migration into Britain. One particularly interesting sub project is their exploration of the use of first names as a research tool. Naturally, first names don't track genetic trends, but they can be used to measure cultural trends (such as the spread of non-Irish first names among the population of Ireland).
It is this last aspect of the Irish Isonymy Project which leads into a particular line of questions I've had for isonymy research in general. Ever since its inception, surnames have been vetted as a neutral marker for population studies. But are there situations in which selective pressure should be taken into account? I will be exploring this topic in posts to come.