There is actually nothing doubtful about it at all. People rescue animals every day. They also tend to organize when the efforts get expensive, time consuming, and the work becomes more than one person can handle. At that point, they start making things "official." Legal documents can have a temporary working name until a permanent name is chosen. I can't remember the legal term for this, but there is one, and the practice is accepted.
I would not get hung up on the name. You will come up with a good one eventually. Until then, just go ahead with rescue work, and don't get caught up putting the cart before the horse. If you aren't already, you will learn an immense amount by volunteering with local organizations that are already established.