The recommendation to label the fire resisting element itself is intended to assist in identifying the need for fire stopping to contractors that may be, or claim to be, unaware that they are installing services through fire resisting elements. It also helps in that each penetration is labelled with the product used to fire stop which ensures that compatible fire stopping products are used for future fire stopping requirements. Without local labelling, it is often not possible to determine the type of product used by visual examination of the product in situ.
The central fire stopping register assists in project scoping and fire stopping audit and should be sufficiently detailed to include all of the relevant information regarding fire stopping materials used. However, in my opinion a single register is less robust than a central record and local labelling. Without local labelling, it would be difficult to confirm the accuracy of the central record, or the extent of any discrepancies.