This could be due to re-marriage to repesct the new (step-) fathers name. More likely the first child had died though. Infant mortality rates depended massively on social standing (ie. wealth) and location. They were at least 50% for some of my families. I have three Susannah's on one occasion dying.....

and two Richards and Johns in the SAME family and they were reasonably wealthy land owners!

I'm guessing a bit, but what was the date? Middle names really became fashionable and inter-changable with first names after 1800.

If you had a very pious parent you had a biblical names which go out of fashion very fast after 1870 (Origin of Species)!
Also, it was common (at least) in my family that a middle name was used to differentiate between say John Snr. and John Jnr., so up until John Snr.died, John Jnr. could be known even on censi by his middle name first!!! As soon as father/mother dies or he gets his own house, he reverts to the name on his birth cert! Trying to follow these can be an unimaginable nightmare!
HAPPY NEW YEAR,

Geoff.