"Television advertisements for the product featured a jingle offering the boast that they were 'More fun than a pillowfight'. No documentation was ever offered outlining any data on the relative entertainment levels of Sock'em Boppers and of pillowfights, and the claim made in the advertising material has never been considered particularly valid from any empirical point of view."
My guess is that "sock'em" basically means "sock them/him," which could be seen as promoting violence in children. Which, whatever...the kids are hitting each other with big ass things on their hands so changing the name doesn't change the level of violence, but people are weird when it comes to the names things can have.
Although, "socker" if you add the apostrophe like in "sock'em" sounds like "sock her," so maybe my theory is wrong. Or maybe they didn't think that through.
Since someone already mentioned the name association with Rock'em Sock'em Robots, I'm going to say it's because they wanted to encourage equality in regard to domestic abuse. Don't just sock HIM, sock HER too. Sock'er. Ya know? No? Phhhht. Whatever then.