Maybe from the entire "need to be ganged up five-to-one to sink her" kind of thing. Or because her name is synonymous to the Tengu. Who knows.
If we're going by the Battle of the Malacca Strait, Haguro fights like she's possessed by a demon even when ambushed and ganged up on. Then again, she was up against 5 destroyers, so she perhaps had some advantage in throwing weight.
Edit: However, I would like to add that the aforementioned "Battle of Malacca Strait" was originally intended as a specific mission to sink Haguro (Operation Dukedom), so perhaps her notoriety was already well-established by her being involved in the sinking of HMS Exeter at the Battle of the Java Sea and the subsequent sinking of HNLMS De Ruyter and HMS Encounter a few days later.
I-I'm Haguro... A pleasure, too...Haguro-san is a mild-mannered person unlike her sisters, and is very calming to be with.I can't believe some people call her the "demon".I-I'm Ushio, I'll provide your escort for today. A pleasure!March 24th
