Luv is an informal way of spelling love. In British English especially, people write it in notes and texts, and say it as a warm everyday word for the person they are talking to — “Thanks, luv” from a shopkeeper, or “Come here, luv” to a child. It can feel friendly and ordinary, or a little cheeky, depending on who says it. It is not a different word with a different meaning; it is love in casual clothes. Americans are less likely to use it as a spoken form of address. In careful writing, spell love.