There are few examples of this in the Gotham ONS. As the Wikipedia article points out there are a number of reasons for the creation of such surnames, and these two examples seem to have different reasons.
This seems to have started with the name Gotham given as a middle name (i.e. a second Christian name), and then evolved into part of a double-barrelled surname.
In 1824 Ann GOTHAM of Teignmouth married William POTTER. They gave the name Gotham as a second Christian name to four of their seven children. At least 2 of the 4 died in infancy, and I have found no offspring of the other two. But one who did not himself have the name Gotham, judging by the baptismal record, Joseph John POTTER, emigrated to New Zealand and all of his six children had Go(a)tham as a middle name.
All six grew up and married, and of these five appear to have had children, with three seeming to have passed on Go(a)tham as a Christian name to their children, including a daughter, so it is now found with surnames other than Potter.
A fourth looks to have passed the name on, not as a Christian name, but rather as part of the surname: Gotham-Potter. (It may be that some of the other members of the family consider they have a double barrelled surname, but without a hyphen this is not clear and so mis-indexed as Nnn Gotham POTTER).
This seems to have started with an attempt to incorporate Margaret BOWEN’s son Arthur BOWEN, in the family when his mother married his step-father. It has been used somewhat inconsistently. The mother’s death was registered with the name, but the step-father just as a Gotham, and the half-brother was simply a Gotham.
Since Arthur only had a daughter it looks like it will be (or has been) a short-lived name.
These days there is to some extent reaction against what may be seen as a misogynistic practice of surnames passing from the father to his children, and also some perceive marriage as outdated, and so a child’s surname may be less predictable. A few attempt to avoid the problem of which parent’s surname to give to a child by giving a double-barreled surname. I am aware of children being registered with three such names including Gotham so far, there are probably others but I can’t easily find most of those where Gotham is the second part (and so they are not indexed starting Gotham) unless and until they appear in the electoral register.Last updated: 1 May, 2021