I have been searching the literature for information on potential selection in surname dynamics. To date I have not found specific research integrating selection into isonymy research. However, there is plenty on cultural selection for surnames in various contexts. As an example I've chosen this article from the Journal of Modern Italian Studies regarding the attempts of the Italian Fascist government to forcibly acculturate the populace to a nationalistic ideal. In such a case of forcible surname change, what we should see in a study of random isonymy from 1926-1942 is a surname "bottleneck" comparable to a genetic one.
From the abstract - This article places the surname Italianization campaign in Italy's Adriatic borderlands from 1927 to 1943 in the broader context of fascist schemes to promote Italian nationalism and construct the Italian national community. A facet of legislative ethnic engineering, surname alteration policy was common to most successor states in the interwar period. In eastern Italy, while ethnic Slovenes and Croats bore the brunt of forcible acculturation, the measures intended to support nationalist, irredentist and imperial aspirations not to persecute Slavs. The fascist authorities' approach to minorities was more nuanced than scholars have recognized in their attentions to competition between west and east, 'European' and 'Balkan', Italian and Slav.
Hametz, Maura, 2010, Naming Italians in the borderland, 1926-1943. The Journal of Modern Italian Studies, Vol. 3 (15), pp. 410-430.