It’s Castile Place and not Castille Square
I don’t know why everybody is suddenly calling it Castille Square.
I’ve never known it to be anything other than Castile (just the one ‘l’ in English) Place and not Square.
It isn’t square at all, and besides, that kind of area – which is not bound by buildings on all sides and is more of a sort of open space used for a particular purpose (hence ‘place’) – is always referred to as ‘place’ and never ‘square’ in English.
The official address is, in fact, Castille Place – with an erroneous double ‘l’. In English, the Spanish region is called Castile. Maltese gets Kastilja from the actual Spanish Castilia, but Maltese speaking and writing English stupidly take ‘Castille’ wholesale from the French name Auberge de Castille.
The mistaken use of ‘square’, I suppose, is because make-do-and-mend Maltese only has the one word for such spaces: pjazza, which has taken over from misrah.
Update: Giovanni Bonello has pointed out that Valletta is spelled with a double ‘l’ rather than with just the one as in the name de Valette, because when Grand Master de Valette ‘baptised’ the new city, he ordered expressly that it be called Valletta – with a double ‘l’. His order is transcribed in stone and in contemporary official documents.