You register once, independently of how many drones operating in the open or specific category you have. Your registration will be valid for a period defined by your national Civil Aviation Authority after which you need to renew it.
However, you do not need to register yourself if your drone(s):
weighs less than 250g and has no camera or other sensor able to detect personal data; or
even with a camera or other sensor, weighs less than 250g, but is a toy (this means that its documentation shows that it complies with ‘toy’ Directive 2009/48/EC);
A drone is certified when it has a certificate of airworthiness (or restricted certificate of airworthiness) issued by the national aviation authority. In this case it require a registration. A certified drone is needed only when the risk of the operation requires it. So it is never needed for drones operated in the open category.
Relevant regulation: article 21 of EU regulation 2019/947.
Once registered, you receive a ‘drone operator registration number’ that needs to be displayed with a sticker on all the drones you own including those privately built. You must also, upload it into the ‘Drone’s remote identification system’.
Regulatory reference: article 14 EU regulation 2019/947.