To be precise (cos we love dat shizz here), the picture shows a Fairey Three Eff.
It might be explained by the fact that it was the last of the Series III float planes beginning with the IIIA, which was Fairey's third production aircraft of indigenous design. The Seal and Gordon, which were derivatives of the same basic design however, did receive officially sanctioned names (!)
From Gordon Wansborough-White's excellent and at times whimsical book Names With Wings (Airlife, 1995), he also raises the question as to why the Fairey III series didn't receive names. This is what he writes:
"There is a part answer that leaves two mysteries unanswered. Firstly, the Air Ministry became somewhat annoyed with Fairey because they did not respond to requests to submit a name. Names supposedly being so important to the manufacturer, why did Fairey not only fail to suggest a name, but also not answer Air Ministry letters? Secondly, as a result of this, the Air Ministry decided to take unilateral action and proposed that the Fairey III would henceforth be known as the Salmon or Griffin, but it continued as the Fairey III!"
Wansborough-White then goes through a brief history of each mark of the III series, with the statement that the IIIE, a metal version was to be named Ferrett, which led to the IIIF. On the IIIF, he ends with this: "The nearest to a nickname was the 'Eversharp Nose' for the clean entry with the Napier Lion engine. ('Eversharp' was the name of a pencil with a sharp point)."