An
Admin user can change the columns/fields of the Shared Lists/All List by clicking on the
Manage List column icon in the respective list view.

A Non-admin user cannot change the columns of a Shared List
Non-admin can contact the Admin user/List owner to get the modifications done on the list columns.
As a non-admin user you can identify the owner of the List by clicking on the Manage List Columns icon in the Shared List.