Rav Moshe paskens that today in communities that do not have a single Beis Din that has authority over the entire community (which includes the vast majority of non-Chasidish communities around the world) either party has the right to insist on using a zabla Beis Din where each party to the dispute chooses one Dayan and the two chosen Dayanim choose the third Dayan.
In general when the plaintiff opens a Beis Din case he can utilize any Beis Din to file it with against the defendant. But once the defendant gets the hazmana he can respond to it and state he’s choosing a different Beis Din to adjudicate the case.
Of course if both parties had agreed in advance before their transaction that they’ll use such-and-such Beis Din in case there’s a dispute, they’re bound to stick to using that Beis Din. But I don’t see how any frum company can force you to sign such an agreement in advance. You can always refuse to agree to that before you do business with them or if necessary choose to do business with another company.