He takes his cues from Natasha, and from Clint.
He knows he's not the best, but he knows that this is the first time Shield has trusted him with something like this, has trusted him to work undercover, and not mess something up.
He knows there could be problems. Knows that sometimes when they're all at the Towers, that Clint will be different and will only respond to the names Aaron or William or Brandt but he always comes back, and so Thor is not that worried.
He will do his best. He hates the feel of the Midgardian Metal Axe in his hand, and he wishes for Mjolnir once more, but leaves it safe on Asgard, as to not give away his true Identity.
Because if Clint and Natasha and Steve and even Wolverine can do this, so can he.