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You are right that the title "Pharaoh" () is first used in the New Kingdom. Specifically, the first recorded use of the title is in the reign of the 18th Dynasty ruler, Thuthmosis III.
The more generally used word for "King" was nswt (, often abbreviated to ). This is most commonly encountered on offering stella, where the standard offering formula begins:
which is transliterated as "htp-di-nsw" and translated as "an offering that the king gives".
Although "nswt" is often read simply as "King", strictly speaking we should perhaps think of the title as "King of Upper Egypt" (i.e. the Nile Valley). Another title given to the King was "nsw-bity" () which literally means "lord of the sedge and the bee" and which we usually translate as "King of Upper and Lower Egypt" (i.e. the Nile Valley and the Nile delta).
Another title which was given to Egyptian kings was "nb-twy" () which we translate as "Lord of the two-lands", again referring to upper and lower Egypt.
In modern usage, however, people tend to use the term "Pharaoh" for ancient Egyptian kings of all periods.
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