Tasmania Pride is the latest option to drop out of the running, meaning the team will be called either the Tasmania Tridents or the Tasmania Jack Jumpers.

The Pride, Tridents and Jack Jumpers were three of five options the NBL shortlisted after receiving almost 10,000 nominations from Tasmania of suggested names for the team.

The two other options that dropped out earlier were Timbers and Mountaineers.

"After today's elimination of the Pride, we are down to the final two options in the search for Team Tasmania's name,'' Team Tasmania CEO Simon Brookhouse said.

"We've really enjoyed the input and feedback from all Tasmanians during this process and we are now looking forward to the reveal of the name next week."

The name will be revealed on October 1.

Brookhouse has also revealed details about foundation memberships.

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Those memberships will be launched on the same day as the name is announced, with Brookhouse saying they will provide a "great opportunity for all Tasmanians to show their support for their team".

He said memberships would allow people to receive "the first merchandise for the new team" and see them be "able to choose their own seat at the newly renovated DEC" ahead of the team's 2021-22 entry.