The Ptolemies indeed had a complex titulature. They understood their dynasty as "Alexander down to whomever ruled at the time," all of whom (after Alexander, at least) were called "Ptolemaios." The kings didn't self-reference themselves by the place that they ruled, but by their ancestors, so calling them the Ptolemaioi is decently close.
EDIT: here's how Ptolemy III phrased it in the Adoulis inscription, from c. 246, following his invasion of Syria in the 3rd Syrian War.
"Great King Ptolemy, son of King Ptolemy and Queen Arsinoe the Brother and Sister Gods, the children of King Ptolemy and Queen Berenike the Savior Gods, descendant on the paternal side of Herakles the son of Zeus, on the maternal of Dionysos the son of Zeus, having inherited from his father the kingdom of Egypt and Libya and Syria and Phoenicia and Cyprus and Lycia and Caria and the Cyclades islands."
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