Conventional accounts of this plant put the emphasis on the ploy it uses to defend against herbivores, its uncanny resemblance in appearance to stinging nettles. It works!
One may label it a case of convergent evolution. Dead nettles is indeed how it is commonly termed.
I am impressed by other resemblances, at least for French speakers. The two words, lamier for the plant and labiées for its family — at least in French and traditionally — are near-homophones, differing only by the middle consonant, m or b. There are other near-homophones or paronyms, such as lamier/ramier, also in French — a ramier is a dove.
But why lamier in the first place? Obviously from the Latin name lamium, that has carried into English, at least as a scholarly word. Lamium itself stems from the Greek lamia, for a gaping mouth, which is what the flowers resemble.
Another easily identified feature is the square section of the stem. Another kindred plant is Galeopsis tetrahit, thus named — the tetrahit part — for that characteristic. Its common name in English is the square-stemmed galeopsid. More generally, Lamiaceae show such square stems.
I do not recall having previously described an herbaceous plant belonging to the Lamiaceae.
And yet! We are very much indebted to these so-called Provence herbs, for their absolutely delightful odorant molecules, which make them ubiquitous in the kitchen, most often as derived spices: basil, lavender, marjoram, mint, oregano, sauge, the apt-named savory, rosemary, thyme, etc. Mediterranean cooking is inseparable from their use. We are all indebted to Elizabeth David for popularizing their use in English-speaking countries.