Only a legal entity can hold a copyright. However, it is worth noting that your copyright notice is not legally significant, since it has virtually no legal effect. Generally speaking, in an overwhelming majority of nations (i.e., all that have signed the Berne Convention), there is no need to include a copyright notice at all, because copyright is secured at the moment the work is created (i.e., "fixed in a tangible medium") whether or not it includes a copyright notice. If your copyright notice is wrong, malformed, or identifies a nonexistent entity, that doesn't matter in the slightest for the application of copyright. (A malformed notice has consequences for a very, very niche edge case in the United States: you cannot procedurally disqualify an infringer's defense of innocent infringement if your copyright notice is malformed -- however, you might still defeat such a defense in court on the merits of the case even if you can't get the court to dismiss it out of hand.)
Ultimately, the notice doesn't matter. Your license will likely require downstream distributors to preserve the copyright notice, whatever it says, and that's really all there is to it.
You could, for example, use any of the following without hurting the validity of your copyright:
Copyright 2019 Jane Doe
Copyright 2019 The Foobar Contributors
Copyright 2019 Cthulhu the All-Consumer
These are all effectively equally useful, since a copyright notice basically has no legal function. The copyright holder is whoever authored the software; the notice should indicate that person or entity, but there's no real problem if it doesn't.
What matters slightly more (though still not too much in most cases) is what kind of entity owns the copyright in actual fact. In your case, since you have no legal entity to hold the copyright, you and your partner will hold copyright on your respective contributions as individuals. If you had a legal entity like an LLC, you could have the LLC own the copyright -- either at creation time or via transfer after the fact -- and exercising/licensing rights under copyright would be done by whoever has control of the LLC. This means that the copyright would go with the LLC if the company were sold or liquidated via bankruptcy.
In the United States, the lifetime of the copyright on a contribution depends on whether the creator of the work is a natural person or a corporation. Works produced by a natural person have a copyright that lasts 70 years after the creator's death, while works produced by a corporation have copyrights that last a fix length of time: the shorter of 95 years from first publication or 120 years from creation. This type of copyright term (either based on author-lifetime or a fixed term) is set at the time a copyrightable contribution is made. If the copyright is transferred later to a different type of entity, this does not change the lifetime-metric of the copyright that was set at its creation.
