Who made the deal? Is there anything in writing other than the lease? When rent was paid to whom or what organization was it paid? Same question for the security deposit.
If the partnership was a party to the lease (or the lessor, as I understand it), then the partnership has standing to sue. You could certainly sue in both names although you'd have to pay two filing fees and, as I understand your question, your main objective is to get this person out of there. Yes, it matters as to jurisdiction and the merits of your case. Did the individual make the deal? Doesn't sound like it. It would seem logical that the partnership would sue.
California Code of Civil Procedure section 367 states that "[e]very action must be prosecuted in the name of the real party in interest, except as otherwise provided by statute." (Cloud v. Northrop Grumman Corp. (1998) 67 Cal.App.4th 995, 1004.)
The real party in interest is “the person who owns or holds title to the claim or property involved, as opposed to others who may be interested or benefited by the litigation.” (Gantman v. United Pac. Ins. Co. (1991) 232 Cal.App.3d 1560, 1566.)
A complaint filed by someone other than the real party in interest is subject to general demurrer if the defect appears on the face of the complaint, i.e., it fails to state a cause of action by the plaintiff because the claim sued upon belongs to somebody else. (Carsten v. Psychology Examining Comm. Of Bd. of Med. Qual. Assur. (1980) 27 Cal.3d 793, 796.)
Perhaps your real question is whether the general partnership can represent itself in pro per in an unlawful detainer lawsuit? The answer is no, the partnership (as an entity) must be represented by counsel in any litigation.
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, consult with your own attorney.
I believe that my colleague Mr. Chen has correctly surmised the landlord's motivation for filing on behalf of one of the individual partners rather than the partnership, i.e., the ability to maintain the action pro se as an individual plaintiff, but not as a partnership entity.
If the partnership is a general partnership as you say, and not a limited one, then I disagree that the individual partner lacks standing to sue. Under California law, a general partnership imposes liability coextensively on the partners for the acts of the partnership. Thus, each partner is a real party in interest to the contracts of the partnership, and would have capacity to sue individually on those contracts. In turn, you could attack the complaint on the grounds that all necessary parties have not been joined (either the partnership entity itself, or the other general partners individually), but I assess that you could not defeat the complaint based on the individual partner's lack of standing.
That's why the general partnership form is a default form and is generally disfavored over other entities such as limited partnership or corporate forms. To determine if the landlord is a general partnership or a limited partnership, you can request a copy of the partnership certificate from the California Secretary of State. If none has been filed, then the partnership is, as you believe, a true general partnership.