JYJ is known to have separated from TVXQ but they are still TVXQ. JYJ has meaning when inside of TVXQ. It’s as if TVXQ is an incomplete group without JYJ.
Jaejoong: “Time has passed and now we are referred to as JYJ and TVXQ, but that we have our group name as the initials of the members means that we work as JYJ in TVXQ. We do not have any intention to get out from the shadow of TVXQ. Because we are still TVXQ, I do not want the expression of TVXQ’s former member either.”
(T/N: A literal conversion of the language would read “we do not have any thoughts to get out…” and that “I hate the expression of TVXQ’s former member” but they not the best translation because in this context those words are used in their secondary senses. For instance, Koreans may say 보고싶다 that converts literally to “I want to see X” but actually resembles more closely in meaning to “I miss X.” This is a similar instance.)