I had, without Googling, always assumed that the word cappuccino simply meant “little head” in Italian. Capo being head and the suffix making it a diminutive form. However, my BFF Tim Lihoreau suggested the etymology was more involved, having heard Inky Fool Mark Forsyth discuss Capuchin monks (on The Museum of Curiosity recently) and the colour of their robes and how that gave rise to the name of the beverage. That etymology is mentioned in many places, but I think  it’s partly deceived wisdom.
There has to be some sort of connection, but this sounds contrived, reverse engineered, like those tales of why Brits stick two fingers up rather than flipping the bird and it being about the French amputating English archers’ drawing fingers (as if warring nations didn’t simply slaughter each other rather than keeping disabled prisoners!)
Anyway, paintings of the Capuchin monks in their robes suggest that they were the common or garden dark brown, rather than the beige one might expect of a decent milky froth on a cappuccino.
Etymol Online has this to say about Capuchin:
Capuchin (n.) Look up Capuchin at Dictionary.com 1520s, from Middle French capuchin (16c., Modern French capucin), from Italian cappuccino, diminutive of capuccio "hood," augmentative of cappa (see cap (n.)). Friar of the Order of St. Francis, under the rule of 1528, so called from the pointed hoods on their cloaks. As a type of monkey, 1785, from the shape of the hair on its head, thought to resemble a cowl.
And for cappuccino:
1948, from Italian cappuccino, from Capuchin in reference to the beverage's colour and its supposed resemblance to that of the brown hoods of the Friars Minor Capuchins (see Capuchin).
So, in digging deeper I did a quick search of Capuchin monk hairstyles and found this Alamy stock image of a modern-day Capuchin monk…now…doesn’t the shaved crown of his his look a little like a milk froth sitting on top of a coffee to you? (No, offence Brother).
I must confess his robes are beige in that photo though and given that cappuccino was coined in the 1940s, presumably by a cafe barista cutting corners and costs, it could have any etymology they liked, maybe it’s both little hood and beige robes…and tonsurial haircuts.