It’s not a classic pun, which is typically defined as wordplay using homophones. But it is word play in that a potentate is an absolute ruler, yet this one is doing manual labor. Then add in the rhyme, which is strong with onomatopoeia. Their name (Hernia) isn’t relevant to that but adds further humor to the concept.
While I can appreciate the alliteration in their slogan, I originally thought “hernia movers” was supposed to resemble some existing word if I said it really quickly but - nope, I got nothing.
Not a pun as much as a directive but there’s a bakery in Estes, Colorado called “You Need Pie.” After seeing the sign my kids decided that they did, indeed, need pie. The pie was quite good.
You are a Party Pooper, which could be a name for, well, no viable business I can think of.
The now defunct Service Supply Co. (industrial products) for years had a giant logo painted on the side of its building along I-65 in Indianapolis, featuring the slogan “House of a Million Screws”.
There is a Vietnamese restaurant here in Columbus Ohio named 6-1-PHO. Columbus’ area code being 614 and the pho dish already defined earlier in the thread.