I'm assuming we call them "Arabian" Knights today as the closest identifier to their skill and nobility as warriors, akin to European Knights of the same period. Comparatively, you wouldn't call a gladiator a Roman Knight, or a samurai a Japanese Knight. So did they have their own proper identifiers during their time?
I think this answer, given by u/Ambarenya in response to a similar question in this sub answers your question. I’d like to add that I’ve never heard the phrase “Arabian knights” - OP may be referencing “Arabian nights” which is an alternate name for the book أَلْفُ لَيْلَةٍ وَلَيْلَةٌ, (One thousand and one nights).