There is no explicit need to have the same CB for ISO 13485- and MDD- certification, but it makes sense.
There is also no explicit need to have a 13485 certificate for compliance acc. the MDD (but audits would take more time, if there is no assumption of conformity acc. 13485...).
It makes sense to use the same NB for both the MDD and ISO 13485, because you can make a combined audit which costs less time and money.
(I know companies, which have one CB for 9001, one for 13485 and a NB for MDD...)
The best way for striving a "notified" CE-mark is:
a) be sure wchich class your device is
b) choose thed Annex of MDD (Annex II, V or VI plus II or VII)
c) establish a QM system (EN 13485 helps a lot)
d) complete your technical file
e) get certified
You should contact your notified body of trust as soon as possible to discuss the path of certification and some other details.
The time required for the whole certification procedure depends primarily on the ammount of different products to be certified, the number of employees in production and the chosen annex (and at last but not least on the NB
If there were no adverse events
it might be possible to close a file within one month (if everything is prepared and perfect also 2 Weeks are impossible - but doable
[but thats the extraordinary exception, not common practice])