No it is not necessary to use graphic organizer for brainstorming.
Brainstorming is most often a verb, as in "I was brainstorming ideas." Here are a couple of examples as an adjective.The brainstorming team came up with several new ideas.He was a brainstorming man.
brainstorming
brainstorming
The laborious undertaking of brainstorming weakened our morale slightly.
Brainstorming
the process of brainstorming invoves
Group brainstorming is where you are in a group and you all give ideas.
I think you should do a little brainstorming first.
"brainstorming"
You would not use criticizing or dismissing ideas during brainstorming with your group. This can shut down creativity and discourage participation. Instead, focus on building upon each other's ideas and creating a supportive atmosphere for free thinking.
Literally, the brainstorming phase.