Happy National Day
There’re two ways of analysing Happy National Day as a noun phrase.
The more obvious analysis, perhaps, is to treat the adjectives happy and national as premodifiers of the head noun day, hence [ happy national [day] ].
The other is to treat national day as a single head noun, and happy as the sole premodifier, hence [ happy [national day] ]. This is perhaps the better analysis since national day is thought of as a single idea.