Correct type designations

Hawker (Raytheon) Horizon is listed in ICAO docs as HRZN but haven’t seen any tracks on one of these; however the NBAA demo a/c N15QS has recently been seen
flightaware.com/live/flight/N15QS

as HA4T (Hawker 4000 - original marketing name). Is this an unofficial designator?

Also mentioned in the news forum a while back:
Eclipse
Are both ECL5 and EA50 correct?

Thx IN (UK)

The aircraft code you see is what filed. You are probably right about the new designation.