Male Ancestors and Surnames

I talked earlier about a speech by Roy F. Baumeister about how society "uses" men, and one of Dr. Baumeister's central pieces of data was that we who are alive today have far fewer male ancestors than female ancestors. DNA evidence shows that we descend from half as many men as women, largely because of historical functional polygamy.

So, an observation: is the paucity of surnames caused by this disparity? If functional monogamy were more widespread historically, would there be a greater diversity of last names?