In Annex VI of the MDR 2017/745, PART C is stated that
"Devices that are reusable shall bear a UDI carrier on the device itself. The UDI carrier for reusable devices that require cleaning, disinfection, sterilisation or refurbishing between patient uses shall be permanent and readable after each process performed to make the device ready for the subsequent use throughout the intended lifetime of the device. The requirement of this Section shall not apply to devices in the following circumstances: (a) any type of direct marking would interfere with the safety or performance of the device; (b) the device cannot be directly marked because it is not technologically feasible."
So it means, that UDI must be on the device if it is technically possible, otherwise all other information can be separately prepared.