The group forming can be done using "Group self-selection" module on Moodle, you can create your own group and choose its name (e.g. Group #1 or Group A) and you can set a password for joining your group, then through chatting on Moodle or email, students (participants) can discuss to be part of specific group. The number of students for each group will be visible, so if anyone still want to join a group, he/she can figure out which groups still need members
In case there are students who cannot or did not join any group, we will use the "Create grouping" feature of Moodle to automatically generate groups for them.