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Interesting question. Also I did not find an answer searching the various macro packages that define \lhd. I assume, once that name existed, others used it too.
Let's guess what \lhd and \rhd could mean.
- left hand drive, right hand drive ?
- left hand delta, right hand delta?
Left hand delta sounds good to me, since it looks like a delta turned to the left.
By the way, I would not phrase it the way that the normal subgroup symbol is called \lhd, but for the normal subgroup the symbol \lhd is used. But I know that was just meant for explanation. I phrased it that way to stress that symbol names are usually generic or by their look and shape, often not by function. So for my math papers that I write, I would define my own set of macros with name by function, such as \let\nsubgroup\lhd. So I never forget it and the code is more easier to read.