Let the Young People select the name for their sub-section (Troop/Six/Lodge) for a brand new section, given some guidance. Discuss the on-going legacy of the name for the duration of the section, not just individual Young People's attendance and how future Young People will become part of the section and continue the sub-section name.
Troop/Six/Lodges determined, list of sample criteria for name selection (eg. Animals whose young are called "Cubs" like Pandas, Great Whites, Raccoons..., Rivers where Beaver dams might be built)
Give selection criteria to groups. Select a first, second & third choice, aiming to give each sub-section the highest choice they can; ties can be resolved by sub-section leaders playing a game of "Rock, Paper, Scissors" or Section Leaders selecting for example.
Collate results and celebrate new names for groups