"Star Alliance" is a trademarked term in the USA and elsewhere. I am doubtful that US is authorized to display the mark once it exists the alliance. Additionally, exiting *A was a term of the merger deal as proposed to DOJ and continuing to market *A, in addition to being a stupid business move, is likely a violation of the deal.

Doesn't mean that there won't be some piece of *A parephernalia lying around over time, but I will be shocked if it sticks.