two surnames do you hyphen them?

AK

Our daughter will be called Wren Sapphire and we want to use both our surnames so she will be: Wren Sapphire Lillie Betts. My surname is Lillie and I think we need to hyphen it as Lillie could get mixed up with people thinking it's a second middle name. so it would be Wren Sapphire Lillie-Betts do you think that looks better? less confusing?