Loveday f. Old English lēof 'dear, loved' + Old English dæġ 'day'.
According to Withycombe s.n. Loveday, the name was often given to children born on a 'love day', a dies amoris, that is, a day for disputants to come together to try to resolve their differences amicably. The name is not found outside of England, and was most common in Devon and Cornwall.