How do I add the project name to a column (project name) for each item using

I am adding automation / integrations to a project board that is created when the status column is changed in a central ‘masterlist’.

I want to identify the easiest way of updating the value for each project task (item) for a particular column to be the project name (which is the board name).

This will then allow me to pull out particular tasks to a central location and have their source (the project name) visible so that we can see where they came from.

I cant jump from the module to list all items from the board to then updating the right column with the name.