These days, the word "nymph" is a sort of shortcut for referring to a woman with an insatiable sexual appetite, almost certainly due to the word "nymphomaniac," and indeed, the prevalence of the use of the word in the adult entertainment industry hardly needs exposition. Nevertheless, according to ThoughtCo, sex was just a small part of whom the nymphs were. The nature spirits, who appear as beautiful young women and kind of goddesses but not really (Greek religion is complicated), were often lovers or caretakers of other heroes in the story. Indeed, the nymphs were known for being particularly kind to men in general, although it bears noting that didn't always necessarily mean sex was involved.
In the case of Nymphadora Tonks, Rowling doesn't appear to have assigned any significance to it, and indeed, there's little to nothing nymph-like about her character arc. In fact, in the narrative, it's revealed that Dora actually dislikes her name, possibly explaining why she prefers to go by her surname.
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