Don't confuse international law (i.e. the UN Law of the Sea treaty) with the laws of different nations. There is no "international law" that will require you or your vessel to have any license or registraiton or documentation or flagging. However, each nation that you try to visit will have their own rules for the identification and sometimes indemnification (insurance) that is required for visiting vessels. If you can't prove that the vessel is yours (title) and what country you and it belong to--to their satisfaction with documents they are familiar with--then they may either send you back to sea, or arrest/impound the vessel.
If you planning to go to the US and Mexico, you only need to satisfy their requirements. If you are going around the world, you may need to prepare more extensively. Then there are visa or entry requirements, which also differ for each nation.
I think the only "international law" that really affects you, would be the law allowing free passage, or entry for succour due to problems en route past the place.