We've already done similar earlier this season:
The latest Leicester City news as the latest accounts show a deal between City and King Power for the naming rights of Seagrave training ground as well as the King Power Stadium.
www.leicestermercury.co.uk
I believe EFL rules don't allow the transfer of ownership to other companies within the group after Derby and Sheff Wed tried similar with their grounds, hence why we have just done a sponsorship deal.
PL rules are apparently a bit more relaxed on that sort of thing, I'm sure Chelsea have already done it with a hotel or two, so I fully expect us to do the same once we are officially in the PL.
It may not be the right thing to do from a moral point of view but the club seem to know a loophole or 2 in the rules.