If the equipment is under the business's name, then the business owns it. If the business is simply you as a DBA with no formal business entity (like a corporation or LLC), then from a practical standpoint you own the property of the business. If you have a business entity, such as an LLC, then as an owner (member) you may have a right to the equipment upon the dissolution of the business.However, unless there is a written agreement giving them an ownership interest in the property, a guarantor does not have any ownership interest in either the business or the collateral - in this case the equipment.