You don't have to do it, but as long as the Resistance remains faceless without publicly denouncing the First Order's claims, you're going to lose this fight with the public and you need them on your side in the long run. In other words, you guys are going to need pick someone to be your public spokesperson. It can't just be anyone either. They need to be strong, capable of being the symbol of the Resistance, have plenty of charisma without being smarmy, and exude honesty.