In the 1800s and 1900s, most inhabitants of the city wouldn't have been able to claim ancestry here, the melting port of the growing port, influx of Irish, Scots and Lancastrians meant most families were fairly 'new' to the area. The 'Dickie Sam' was therefore the character of a Liverpudlian ( or Liverpolitan as it would more commonly have been known), rather than birthright.
There are several possibly attributions for the name ‘Dicky Sam’, and as is often the way, the most common is the most unlikely.
Most commonly descriptions say it is after Dicky Sam's, public house at the pierhead, but this is putting the Sam before the Dickie. The pub was named after the term ( which pre-dates it) rather than the other way around.
The most popular justifications are from Lancashire dialect as a way of putting the inhabitants down, using the transatlantic trade links to create Dicky Sam as a poorer relation of ‘Uncle Sam’. Or as a ‘bog dweller’, as I’ll explain.
The spelling by the way, does vary in different accounts. Which is 'correct' would depend on the real derivation of the term, which we will never definitively know. But as I like you, I'll give you a hint as to my own interpretation:
Looking at the length of time the term ‘Dicky Sam’ appeared for, and its acceptance as 'common parlance', it is likely the term was originally a very old monicker. The celtic derivation for Fen Dweller, or Bog Man ( dighe samhadhe) is particularly pertinent to Abercromby Square, but the whole area surrounding Liverpool used to be heathland and fenland. Before 1700 fellow Lancastrians looked down on this minor port and its commerce, or lack of it (despite relying on the then Town for the Irish trade themselves), so associating the inhabitants with the ‘land of bogs’ is quite conceivable.
The links to America, and the later creation of the 'Uncle Sam' moniker ( allegedly after a New York meat dealer) might naturally have lead to the adoption of ‘Dicky Sam’ in a new context over time. It is certainly true that the close links between Liverpool and America were claimed wholeheartedly and proudly by Liverpolitans.
Outside Liverpool, ‘Dicky Sam’ was used as a term of insult for exactly the same reason. Just as a 'dickey' is a fake shirt, inhabitants were seen as wannabe Americans by some of the London merchants, hence 'Dicky Sam' as a term both of affection and derision.