Not all engines do. i had a 78 Olds and the engine serial was on a paper sticker that eventualy fell off.
For your purpose you could just peen a tiny punch mark somewhere
and take a picture for piece of mind.
serial numbers are usually stamped on the top of the block next to the cylinder head , Haynes and other manuals usually tell you where they are
yes there are serial numbers on engines
I'm having an independent mechanic swap out an engine for me. I bought an engine from a salvage yard with only 75k on it. I want to make sure the guy doesn't just go back to another yard, get one with 250k on it and keep the 75k engine. I'm wondering if there's any unique #s on the engine to be able to determine that it is in fact the engine I ordered.