While his older brother, MINAMOTO no Akikuni, inherited their father's pseudonym "Tada", Nakamasa took "Baba" as his pseudonym; therefore, he was sometimes called BABA no Nakamasa.
兄の源明国が父・頼綱の号である「多田」を継承したのに対し、仲政は「馬場」を号としたため「馬場仲政(ばば・の・なかまさ)」ともいう。