I remember there were some voices in this forum arguing for China to change the name of PLA to "China Army, Navy and Air force". I just read the recent news about PLA air force giving warning to Taiwan's pilots as "This is People Liberation Army......". It won't work if the name is changed that would effectively makes the two sides' air forces from two countries.
Just a practical reason for not changing besides the more important reason "the nature and root of PLA". There was same suggestions in the early days of PRC which was rejected by Mao because "China's land is not fully liberated yet", he further stated (partially joking) "even after the whole China is liberated, there is the world to be liberated."
When the PLAAF intercepts foreign aircraft the pilot always says that "this is the Chinese Air Force".