All class I medical devices according to the MDR, from today, have to be in compliance completely with the MDR Technical requirements (Annex 2 _ Technical documentation). One of those requirements is to have an MD symbol on the label. For details on what needs to be on the label, please see section 23 of Annex 1 – General safety and performance requirements.
Yes it is, it is stated in the Annex I General safety and performance requirements, section 23.2 The label shall bear all of the following particulars: q) an indication that the device is a medical device
It is not forbidden to put it on the MDD compliance device, but it means that you need to implement ISO 15223-1:2021 into your system, so all symbols that are required in that standard and applicable for your device should be implemented. Also, it means that you need to change your essential requirement checklist with this new standard.