[EricH]

I propose that they just go back to what they used previously.

Let the divisions be letters A, B, C, D, E, and F.
Let the teams that register be 1, 2, 3, ..., n, sorting by numerical order.

1 goes in A, 2 goes in B, 3 goes in C...6 goes in F, 7 goes in A, 8 goes in B...n goes in the next-in-sequence of A-F.

Assign A-F to random division names.

The problem (or not) with this method is that anybody can generate a division list with a few minutes and some programming knowledge, and knowing which teams are signed up.