So there are four Houses (and four Founders): Hufflepuff, Gryffindor, Ravenclaw, and Slytherin.
Hmm. HGRS. What does that spell? Oh right! Hogwarts!
Did J. K. Rowling do that on purpose?
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There’s nowhere that JKR ever mentioned that the name Hogwarts contains the initials of all the Founders, or whether this was intentional.
Relying only on logic and common sense, since there’s no “official” information on this, it’s hard to reason out a definitive answer in this case. It’s entirely possible that it was intended, but it’s not sufficiently clear that it can’t plausibly or reasonably be seen as unintentional (like how Diagon Alley is clearly a pun on “diagonally” even though that’s never “officially” confirmed).
A google search showed me this tumblr page , where a potterhead defines this connection as
H G R S Is in Hogwarts for a reason, and that reason is House unity.
There are also other sites showing this connection, but couldn't find any official J.K. Rowling announcement. So after reading why Hogwarts is named Hogwarts ? I believe that she found the name Hogwarts first and then derived the house names from it. Not the other way around.
But I didn't see that connection until I read this question. I read every book minimum 3 times(if not more)