I have four thoroughly reviewed novels right now and I am wanting to copyright them before May 2020. But, I am having doubts as to whether or not I should. I am aiming for traditional publication and am actively seeking a literary agent. Should I just wait until my publisher copyrights them? Will they copyright them under my name or under the company? Thanks.
Writing is automatically copyrighted when it is "fixed in a tangible medium", so save it on some form of drive you own with a date (do not self-publish it; most agents will not take you on if you do). It does not need any formal notice of copyright at any stage, even a copyright symbol; registering it with the US Copyright Office would only be useful in making it slightly easier to sue someone who steals your work, but if that happened any copyright lawyer would know that you are in the right and not the plagiarist. If it came to that, you'd win even if you hadn't registered.
Unless you believe you are at imminent risk for someone stealing your work and publishing, don't do it now. This is part of why you get an agent. They're the ones that negotiate with publishing companies and deal alongside them with the technical logistics of your work, including copyrighting, formatting, etc. Contracts differ, but I no reputable agent would let you go forward with one that didn't copyright your work to you as the author. Publishers take out copyrights in the name of the author. They handle the legal and paperwork side of things, but the copyright would be your own.