RebE, mazel tov!
Yoma addressed the issue of Chief Rabbis at the end. R Hanina refuses to accept an apology from Rav for 13 years because he saw a dream that Rav will be a Rosh Yeshiva (hanging on a palm), so he did not want to retire or die, and made Rav make yerida to Bavel where he became the Rosh yeshiva. So, this is clear that there is one Chief Rabbi at a time, Israeli and Russian customs notwithstanding.