Witty & Playful:
* Wordsmiths
* Crossword Crusaders
* Puzzle Posse
* Grid Gurus
* Cipherers
* The Clued-In Crew
* The Word Wizards
More Formal:
* Crossword Enthusiasts
* Crossword Solvers
* Crossword Club
Ultimately, the best name will depend on the specific group's personality and style. You could even get creative and come up with a name specific to your group, like "The Ink Slingers" or "The Clue Crackers."