Hidekatsu could have been elected as a real heir of Hideyoshi, if Hidekatsu had lived long, but considering that Hideyoshi was appointed as Kanpaku (chief adviser to the Emperor) in 1585, the same year Hidekatsu died, it seems that Hideyoshi no longer needed the name of ODA.
秀勝が存命していれば彼が後継者となった可能性も十分にありえるが、ちょうど秀勝の死んだ1585年に秀吉は関白となっており、もはや織田の名分は不要だったとみることもできる。