Yes, although it hasn't worked out like that (in answer to OP).
Ds1 was stillborn (apologies if it seems I am always talking about this). Dh didn't want him to have a middle name so we didn't choose one. Ds2 born 9m later, but I refused to give him a middle name, as wanted both boys to be the same. With hindsight REALLY REALLY wish had given ds1 dh's name as middle, and ds2 would then have got ds1's as middle. Strangely dd does have middle name, as felt differently about it then.
Dh has a cousin with the same name as him, and another whose middle name is same as dh's first, which I just find weird. Another cousin's wife had a baby before xmas, when I asked about names when she was pg, he said "X (ds's name) for a boy, or Y (dd's name) for a girl"!!
Luckily they called him something else. Weirdos.
Also know of a man with 4 sons, all with middle name of James. Youngest is my godson, and his mum found out he had called his teddy James as a middle name, as he thought it was compulsory! PMSL 