The word layan is not in the Quran, but its verb praises the gentleness of the Prophet ﷺ: “It is by a mercy from Allah that you were gentle (linta) with them; had you been harsh and hard-hearted, they would have scattered from around you” (3:159). Allah also commanded Musa and Harun to speak to Pharaoh “with gentle words (qawlan layyinan)” (20:44).
Meaning of the name Layan
Layan is a verbal noun of lana, “to be soft, supple, gentle” (root l-y-n, that of lin, “softness”, and layyin, “soft”); lexicographers quote the phrase huwa fi layanin min al-ʿaysh, “he lives in softness”, that is, in ease and comfort. The name evokes a gentle character and a life free of harshness. A recent name, it is very popular for girls in Saudi Arabia, Jordan and Palestine.
So by mercy from Allāh, [O Muḥammad], you were lenient with them. And if you had been rude [in speech] and harsh in heart, they would have disbanded from about you. So pardon them and ask forgiveness for them and consult them in the matter. And when you have decided, then rely upon Allāh. Indeed, Allāh loves those who rely [upon Him].
Allāh has sent down the best statement: a consistent Book wherein is reiteration. The skins shiver therefrom of those who fear their Lord; then their skins and their hearts relax at the remembrance [i.e., mention] of Allāh. That is the guidance of Allāh by which He guides whom He wills. And one whom Allāh sends astray - for him there is no guide.