On the latest edition of Wrestling Observer Radio, Dave Meltzer revealed that after last night's Bash at the Beach event, The Elite gave a speech to the crowd which saw them mention getting into a legal battle for using that name for this special episode of All Elite Wrestling: Dynamite.
WWE acquired the name after buying WCW but Cody Rhodes was able to trademark it last year along with other WCW PPV names that were created by his father.
It's possible that WWE could be looking at taking legal action and that some sort of agreement may have been reached but it seems pointless for them to go after All Elite Wrestling like this, especially when it's not like they had plans for the name!
The difference between AEW and other promotions is that they have the money to fight WWE in court so chances are this simply won't be worth pursuing.