The Berings do not, in fact, have any sons. It was so named, according to Myka, because it sounded more refined and elegant. It would also seem plausible, given the adversarial nature of the interaction between Warren and Myka, that there was some intention of goading her into proving herself better than some hypothetical son, or perhaps even the hope that she would look to have her children take her maiden name in order to "fulfil the prophecy". Whatever the intent, however, the real-world result is generally to make Myka believe that she has once more disappointed and failed her father, a spur which has constant and profound ramifications on her career as a Secret Service Agent and her relationships, above all with Artie.
It is interesting that the bookstore still exists and retains its name in the alternate reality of "The Greatest Gift", since Warren has passed away, and the chasm between the remaining, female, Berings seems unbridgeable. Jeannie, however, answers the phone here with "Bering & Son Books", a singular which may have some significance in her mind, as Myka's, and others', reactions make it clear that Warren did not encourage "girly" behavior in his eldest child. Pete even commented, in "Mild Mannered", that she must have touched an artifact "that made her act like a girl", when Myka displays an understandable joy at being reunited with her possessions, and thus able to make her room at Leena's feel like home.