The correct answer is A) with the vessel's name. According to the small passenger vessel regulations, all life jackets carried on board small passenger vessels are required to be marked with the vessel's name. This is to ensure that the life jackets can be easily identified as belonging to a specific vessel, which is important for safety and accountability purposes. The other answer choices are incorrect because they do not align with the specific regulatory requirement for life jacket markings on small passenger vessels. The life jackets are not required to be marked with the vessel's official number (B), the maximum weight to be held by the life preserver (C), or the maximum serviceable life of the life preserver (D).