I could be wrong but my bet is, they will continue with the name Linkin Park but will not take a new singer. I feel like even if they revived some legendary singer from the dead who could sing the songs to a perfection, he would still get booed off stage. That is how much people loved Chester and they would see replacing him as a spit to the face. At least right now and near future, i don't think people don't want to hear the old tracks sung by another singer. It would feel like "too soon" and weird. Playback for Chestert's vocals feels the correct thing to do for the moment to pay a tribute.
About the name change, we need to understand that it's not as simple to just change the name. Linkin Park is more than just a name. It's a brand that the guys have worked on for many years to achieve this massive level of global reach. I have never met someone who doesn't know Linkin Park. There's a reason STP didn't change their name either. It's not to disrespect anyone, it's just the way it goes in this business. Nobody will ever forget Chester and what he has done with the band.