Trigger table name as variable into stored procedure
MySQL provides no way to do what you want.

The obvious suggestion would be to modify the triggers and the procedure to add one more parameter, which is the table name. But since it's obvious, you probably don't want to do so. Probably because the triggers and the procedure run in production, and they cannot be updated atomically (so if you modify the procedure first, triggers will fail; but if you modify a trigger first, it will fail).

If that it the reason, I suggest to use a user variable. In the triggers, you can do something like:

SET @table := 'wood_table';


And in the procedure, you will be able to check the value of @table.