Lol Most wont understand your clever post.
I got it. Tso funny.
Maríaluisa David, B.A. Cultural Anthropology & Culture and People of Mexico, University of California, Los Angeles (1978)
Updated July 27, 2018
Diné (Navajo) people did not traditionally have family names. Instead they were identified with a personal name and the name of ones mothers maternal clan (born to Black Rock). The name of the persons fathers clan is the clan one is born for-born for Red Forehead). For example, in Navajo, I would be identified as:
Mary, born to the Black Rock, born for the Red Forehead. Diné people are strictly matrilineal so one is always born into ones mothers clan.
When white people began to colonize Diné people and the Diné land, they demanded that Diné people use the naming traditions of white culture. People acquired family names in a variety of different ways. Begay means simply his/her son. Edit: the more correct word in Diné for her son is biyáázh bee-yahj. People identified their family as to who their mother was. Of course what they were saying was misinterpreted as being the name itself. Someone might say Sam, biyáázh MarySam, Marys son. The Diné language in common with many indigenous American languages uses gender to denote the gender of the person speaking as well as the gender of the subject. Its a perfectly reasonable way to identify ones family. But white Americans imposed their naming traditions and the Begay family was born and babies began to be identified into families as to who their fathers were, a concept totally alien to the Diné way of thinking.
Another way that Diné people acquired family names was through schools. When Diné kids were first taken to the schools, they were assigned white names such as Tom, Billy, or my own last name, David. That generation of kids, my great-grandfathers generation, did not have family names necessarily. When the next generation went to the schools, they were asked what their fathers white name was. The first name of the students father became the family name. In my case, great-grandfather went to white school and was named David. When grandfather went to school, he was assigned the name Lee. Since his fathers name was David, grandfather became Lee David. When my father went to school, his name was John David. As his daughter, my name is Mary David. One of grandfathers brothers name was changed by a white school staff to Davis instead of David. So family members have a variety of family names including David, Davis, Black Horse, Tauglechee, and, unsurprisingly, Begay. Someone became confused and identified their mother rather than their father. In the Diné language it was begay Rachel. The cousin meant Rachels son. School officials heard the ubiquitous name Begay.
So to succinctly answer, the name Begay is a common one among Diné people because it was misunderstood by white people attempting to impose their style of naming. It is not a name in tribal groups other than Diné.
That's the idea. Good one.