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I believe if the host doesn't require signups it means anyone can begin playing at any point in the game. The host will include choices from whoever's suggestions have been posted at the time they begin the the next round.

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e.g. ROUND 1 Player A, B, and C join in and respond with name choices.

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ROUND 2 host chooses names from Player A, B, and C's responses from ROUND 1, and reveals them adding rules for ROUND 2. Player D joins in at this point (having submitted options for ROUND 1, but the host doesn't go back and consider them). Players A, B, C, and D respond to ROUND 2 which choices.

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ROUND 3 this time host chooses from Player A, B, C, and D's responses and so on with whatever combination of players that have responded by the time the host is ready to move on with the next round.