It's possible or not

Hi, I have a board with a bunch of items. When I change the status (or another field), I would like an item to be created in another specific board, but only if that board’s name matches the item’s name.

If there isn’t a board with that name, I would like a new board to be created with the item’s name, and then the item added there.

Is this possible?

yes, it’s possible. you will have to make a webhook to a url and backend code can use Monday API to get matching board and make decision of creating new board and a line item.