One thing Marvel fans may be asking themselves after watching the first trailer for Thunderbolts* is, "Why is there an asterik at the end of the name?" It's definitely an interesting question, especially because the asterik was added last year after Marvel Studios made some adjustments to its release calendar. Marvel Studios President Kevin Feige even confirmed the asterik was an official part of the Thunderbolts* title, though he didn't elaborate on exactly what it means. Of course, that isn't going to stop us from speculating, and there are some clues that point us to some adaptations from the comics that are tied to the Avengers.
Thunderbolts* features a diverse cast of characters, headlined by Florence Pugh (Yelena Belova), Sebastian Stan (Bucky Barnes / Winter Soldier), David Harbour (Alexei / The Red Guardian), and Julia Louis-Dreyfus (Contessa Valentina Allegra de Fontaine). As Yelena referenced in the trailer, every member of the Thunderbolts has a shady past. After the conclusion of Avengers: Endgame, there doesn't appear to be an official team of Avengers operating in the MCU. This leaves a void that the Thunderbolts are perfectly suitable to fill. Valentina may also be the person who purchased Avengers Tower, which is another clue to the Thunderbolts* asterik. What if the Thunderbolts are meant to replace the Avengers, even taking on their name?
Following the Secret Invasion event, which saw the alien Skrulls infiltrate and attack Earth, Marvel Comics transitioned to its "Dark Reign" publishing initiative, with Norman Osborn put in charge of the global peacekeeping entity known as S.H.I.E.L.D. Norman renamed S.H.I.E.L.D. into H.A.M.M.E.R. and dressed up some of Marvel's most infamous villains as fan-favorite heroes, dubbing them the Dark Avengers. Norman gained this rise in prominence by helping to defeat the Skrulls during Secret Invasion.
Tl, dr: nobody knows yet.