In "The Rocking-Horse Warrior," it is fairly easy to determine the symbolic meaning behind D. H. Lawrence's choice of the name Bassett for the servant who helps young Paul. First (all names courtesy of ThinkBabyNames.com), it is an Old English descriptive name (name that originally described the person to whom it was given) that was and is still rare in contemporary society. Bassett's personal qualities--honesty, respect toward a child, belief in a child's abilities, dependability--are rare qualities, as rare as the occurrence of the name. Additionally, the name meaning is "little person." Bassett is indeed a symbolically little person in that he is only a servant and, in a servant/master societal structure, therefore a person of little importance.
The symbolism behind Lawrence's choice of the name Paul is also fairly easy to determine. The meaning of the Latin origin name Paul is "small." Being a child, the name Paul is therefore symbolically appropriate. There are several historic associations with the name Paul. The most significant is the association to the Apostle Paul of the Christian religion. It is said of the Apostle Paul that he was the "rock," or the foundation, of Christianity. In addition, popes of the Catholic Church have been named Paul. These historic Biblical associations add symbolic meaning to young Paul's character by emphasizing his innocence and goodness and pure altruistic motives.
Uncle Oscar is a lot harder to sort out. Aside from being the biological relative through one's mother or father, Collins English Dictionary says "uncle" is a term of address used by children for adult males who are friends; they would therefore have the child's best interests at heart. The name Oscar is an Old English name meaning "spear of the gods." It may have originated in an old Gaelic phrase meaning "friend of the deer." Let's see if we can sort this out.
"Uncle" is definitely used ironically: Oscar was meant to be Paul's friend but betrayed Paul's trust and forsook his custodial responsibilities to Paul. Therefore the title "uncle" points to the tragic irony of Oscar's relationship to Paul. If the "spear of the gods" is intended to punish and strike down, then this is symbolically fitting of Uncle Oscar, as he does strike Paul down through his manipulation and disregard. Again calling up tragic irony, Uncle Oscar was meant to be the "friend of the deer," was believed to be the "deer's" friend, but did not act the part of the friend. Rather, he acted the part of the user and manipulator. So two-thirds of the interpretation of Uncle Oscar's name is ironic and one part, "spear of the gods"--the negative part--is direct.