Each of these fields has one number that means something and several that look as though they do.
Vessels. The IMO number is seven digits, assigned once, and never changes for the life of the hull — through every sale, rename and reflag. That is what identifies a ship. The name changes, sometimes yearly. The flag changes. The MMSI changes with the flag and is a radio identifier, not a ship one. A vessel that has been renamed four times and reflagged twice has one IMO number throughout, and searching the name finds none of it.
Companies. The registration number in its own national register is the identifier; the name is not. Companies are renamed, and names repeat across jurisdictions freely. An LEI identifies an entity that was issued one, which is a small minority of companies worldwide — its absence means nothing at all. Note also what a register actually records: the person named as director on the date it was last written to, which is not necessarily who controls the company and not necessarily who did last month.
Sanctions. A designation is an administrative decision by a government, not a conviction. Lists carry aliases and transliterations precisely because name matching is unreliable, and a "possible match" on a sanctions list is the beginning of an enquiry rather than the end of one. Delistings happen and are much quieter than listings, so check the current list rather than a copy — and check the date on whatever you are reading.