how to find the last name of a business owner?

If you are suing an individual and can't find his/her name, you would generally (in the jurisdicitons in which I generally practice which doesn't include NM, but it's probably the same there) sue "John Doe", who you would identify in the caption and the body of the complaint as the business owner.   If this business is a corporation, llc, or other legal entity, you would generally have no basis to sue its owner or owners personally; as a general rule, the owner or owners of a corporation, llc, or the like, would not be personally liable for its obligations.  That is probably the main reason why people incorporate.