Alibaba Group Ltd. can push forward with claims that an unaffiliated cryptocurrency firm calling itself Alibabacoin Foundation is infringing its trademark, a federal judge ruled.

Alibabacoin’s arguments in its motion to dismiss the complaint had already been considered and rejected by the The U.S. District Court for the Southern District of New York when it granted Alibaba’s motion for a preliminary injunction, the court said Nov. 7.

It’s tougher to win a preliminary injunction than a motion to dismiss, the...