Oswald of course did exactly the opposite of what anyone would do if they "wanted to be known as" killing the President.
When in custody of the Dallas police he continually denied having anything to do with the killing of the President, or police officer Tippit [who a man fitting Oswald's description shot Tippit just after the assassination].
Not only did Oswald continually deny everything, but the Dallas police detained and questioned him without any counsel despite his continual requests for such. Additionally the Dallas police kept absoutely no records of any kind of his questioning.
This bizarre and bungling behavor by the Dallas police was the genesis of the Warren Commission. In a phone conversation with President Johnson days after the assassination [available at the LBJ library] Dean of the Yale Law School Eugene Rostow stated that not only did the general public not believe that Oswald did it, but that attornies, judges and officials countrywide were also unconvinced,
Rostow:
"The way the Dallas police have handled this no one believes anything we say about it."
It was this counsel by Rostow which convinced Johnson to create the Warren Commission. At the same time, Eugene Rostow's brother Walt was in the White House as the Deputy National Security Advisor to Johnson. He was in the process of drafting a Presidential Directive for Johnson which was signed the following day. That was the Directive which reversed a former one signed by Kennedy weeks earlier mandating the withdrawl of all U.S. combat personnel from Vietnam.
Walt Rostow became Johnson's NSC advisor, and never wavered from his support of the Vietnam war. Consequently after 1969 he had nowhere else to go other than his boss's new graduate school in Austin. He therefore remained there as a Professor until he died in Austin in 2004. Disgraced in acedemics, he contented himself with teaching and doing research in the LBJ library. However in 1981 he became re-energized when his buddy from CIA, William Casey, became the Director of Central Intelligence under Ronald Reagan. He began spotting and recruiting students for intelligence training and careers. One of the places such students went was Pakistan, from which the war in Afghanistan was supported....and still is....all these years later.