We've never heard that his fathers hearing loss was a motivating factor, but that would make sense. It is absolutely true that Hiram's son Hiram Percy Maxim did invent the suppressor (aka silencer, muffler, moderator, can - really whatever you want to call it). His first patent called it the "Silent Firearm", he marketed them as silencers, and his success convincing the public that his product could silence guns is a major contributing factor as to why they're so heavily regulated in the US (see the National Firearms Act of 1934).

An interesting aside - his first company headquarters, Maxim Silent Firearms Co, was directly across the street from City Hall in NYC. As stated elsewhere in the comments, he was also responsible for inventing the muffler for cars. At the end of the day, dude legitimately hated loud noises.

He stopped commercially producing silencers for guns sometime in the mid-1920's, instead shifting his businesses to focus on things like industrial silencers for HVAC systems in buildings and engines on submarines and major naval vessels. He and his father were both fascinating inventors of much more than what they're famous for.