Pet errors are related ot how the default Blizzard UI handles the pet panels now. There's nothing on MRP's end that's possible to "fix" these errors.
Same goes for the character names. There's a pause between login and addon loading that sends data to the communication channel. There's no way to hasten this interaction without causing the players to flood the channel and cause lag to the chat servers for the realm you play on.
You will run into [XxIllidankxx] says: "I gave up my life to stop the burning legion." instead of [Slayer Xandius Starfallen] says: "I gave up my life to stop the burning legion." when you first load into a character regardless of changes made to the addon.