I have no middle name but my younger brother does. When friends at school asked why, I spoke to my Dad and he told me it was because they didn't have much money when starting out as a family but had saved enough up by the time my brother was born. I dutifully reported this back to mates who must have assumed I'd lost the plot but didn't bother telling me.
I asked my Dad about it many moons later and he said that he and my Mum had decided to dodge convention and not give us family names (despite intense pressure from my Dad's mother to name me after my Dad and his father and his father). It all went swimmingly until my brother was born and then, immediately after his birth Mum declared he was getting her father's name as middle name and Dad didn't think it was a hill worth dying on. He did say I was welcome to change my name to include a middle one but I didn't think it was worth the hassle. In hindsight I should have agreed and said I'd have his name as my middle name. Ah well.