The 'lady' part of the name is a reference to the Virgin Mary (Our Lady/Notre Dame idea). The 'bird' part just refers to this particular beetle's ability to fly, so - as a whole - the name means "The Virgin Mary's flying creature". 'Ladybug' is also used, especially in the USA.
the latin name is Coccinellidae.
In various parts of Britain they have been given other names; in Lancashire they are known as 'God's Horses', in Wales they call them the 'Red Cows of God', in Lincolnshire they are known as' Lambladies', in Yorkshire they are often called 'Dowdy Cows' and in Norfolk they're known as Bishy-Barny-Bees.
http://www.uksafari.com/ladybirds.htm
Thanks for your answers, they're very interesting. Lard, my dad and a lot of my family live in Norwich and I've never heard of them called bishy-barny-bees!