Going to change my PS4 for a new one because of a hardware problem, I have a question regarding installed games

Hey guys, I have technical question for you, maybe you can help me:

I bought a new PS4 bundled with 3 games inside the box at a retailer, but the console came with some sort of hardware failure: every once in a while when I turn it on by pressing the power button, it will either turn off almost immediately, go into safe mode right away, go into an uncontrollable restart loop, or all of them combined.

I'm going to change it tomorrow at the same reatailer. My issue is actually with the games. I installed them so I'm worried that when they give me the new console with the new 3 discs I won't be able to play them because maybe the previous installs were registered at my Sony account or something (the one I select when I start the console). I don't yet know how DRM works in these consoles.

Maybe it's a super noob question but since I'm new with these new gen consoles I want to be sure about everything. Having to change the console for a new one after spending so much money is quite a headache already.