The latest push for Statehood includes the intention to use the name; Washington, Douglass Commonwealth, a reference to African-American abolitionist Frederick Douglass as detailed on Wikipedia though different names have been suggested in the past.
For most of the modern (1980-present) statehood movement, the new state's name would have been "New Columbia", although the Washington, D.C. Admission Act of 2020 refers to the proposed state as "Washington, Douglass Commonwealth."
1 - Council of the District of Columbia. March 10, 1981
2 - H.R.51 - 116th Congress (2019-2020): Washington, D.C. Admission Act
A different name again appeared on the ballot to residents when asked about statehood.
On November 8, 2016, the voters of the District of Columbia voted overwhelmingly in favor of statehood, with 86% of voters voting to advise approving the proposal. Although the proposed state name on the ballot sent to voters appeared as "State of New Columbia", the resolution passed by the D.C. District Council passed in October 2016, weeks before the election, changed the name to "State of Washington, D.C.", in which "D.C." stands for "Douglass Commonwealth", a reference to African-American abolitionist Frederick Douglass, who lived in Washington, D.C. from 1877 to 1895.