Sppedbird, Moonflower, Dreamjet: the 'secret names' of the companies. Who uses them and what they are used for
In English they are called 'callsigns' because they are the names that are used by pilots and air traffic controllers [...]

In English they are called 'callsigns' why are the names that are used by pilots and air traffic controllers To identify the airlines During radio communications.
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Basically, they are 'nicknames,' nicknames officially recognized by the ICAO (the global body that oversees air transport) and which are used to make radio communications simpler and more effective (and foolproof), especially In cases where airlines have long names or names composed of more than one word, which could 'confuse' those communications, especially in 'demanding' phases of flight such as approaching particularly busy airports.
Some of these nicknames are rather trivial, some are more creative, and some are even fascinating. The best known of all, perhaps, is the one used by British Airways: 'Speedbird', which literally translated means 'bird of speed.'
Hearing pilots and controllers speak on the approach to an airport or even during taxiing, we would not hear them say 'British Airways 236' (to give an example), but 'Speedbird 236'.
Aeroflot remains 'Aeroflot', Lufthansa simply 'Lufthansa' (because in these cases a nickname would simply complicate things). E so it works for all or most vectors whose name consists of a single word (Condor, Iberia, Qantas, just to name a few examples).
However, precisely, there are several truly original 'callsigns' circulating in the ether. Thus, Aer Lingus becomes 'Shamrock' (which is the shamrock, the symbol of Ireland); Air Asia X (the long-haul branch of the Malaysian low-cost carrier). 'Xanadu'; Brussels Airlines becomes 'Bee-Line'.
Lot Polish Airlines becomes 'Pollot'; the Italian Neos and ITA Airways become respectively 'Moonflower' and 'Itarrow';
Norse Atlantic Airways becomes 'Longboat' (from the 'long boats' of the Vikings who first crossed the Atlantic).
And, again, the low-cost tuca Pegasus Airlines 'Sunturk'; South African Airways 'Springbok', named after the gazelle that adorned its tail in a vintage livery of the South African carrier; the Taiwanese Starlux 'Starwalker'; TUI fly Belgium 'Beauty'; Virgin Australia 'Velocity'; the all-Business La Compagnie 'Dreamjet' (perhaps because The one on his planes is a dream flight?); the low-cost Japanese Zipper Air Tokio 'Zippy'; Thai Lion Air 'Mentari'; easyJet simply becomes 'Easy'.