Napoleon the III was the third son of Napoleon’s stepdaughter Hortense and Napoleon’s brother Louis. He was the third son of Hortense’s to essentially be named Napoleon. Louis had attempted to give his son’s other names but Napoleon over powered him. Napoleon was extremely possessive of his stepdaughter and this among other reasons led to extreme anguish in Hortense’s life. With the unhappy couple’s third son, Louis at least was able to get his name placed before Napoleon’s so this is how Louis Napoleon Bonaparte’s name came to be.
Louis Napoleon was forced to leave France as a boy as a consequence of his mother’s loyalty and strong association with the Emperor. Napoleon basically had been treating Louis Napoleon as his son (until Napoleon was forced to leave him).
Louis Napoleon was raised by his mother to honor and vindicate Napoleon. I don’t have the depth of knowledge about Louis Napoleon as I do his uncle in part because there is really a lot of disinformation about him.
This is Hortense with her oldest son who died. In her stupefaction over this child’s death, she allowed her husband to do what he wanted with her (she did not like him and was being abused by him) and this resulted in her pregnancy with her third son Louis Napoleon. Strange but true.