We don't know. Strictly speaking, we don't even know if "Greater Phrygia" was a meaningful administrative division in the Achaemenid Empire (a place where minor administrative divisions changed regularly).

It certainly wasn't a true satrapy in its own right. "Phrygia" - as in most of inland western Anatolia - was governed as part of Lydia. The Kingdom of Lydia became a satrapy after being conquered by Cyrus the Great but functionally retained its independent borders. The Old Persian name for Lydia was Sparda, which comes from the indigenous Lydian name for their own king: Sfard. "Lydia" was the Greek name derived from Luwia, the early Anatolian name for the same region and the Luwian people/language. When the Persians referred to non-Greeks from that part of Anatolia, they just said they came from Sparda.

The more complicated resonse to this question is actually about Hellespontine Phrygia and Tyaiy Drayaha because there's nothing in the Old Persian corpus (or the related Elamite-language administrative records) to suggest that these two names refer to the same place. As best as I can tell, the first person to make that claim was A.T. Olmstead in A History of the Persian Empire (1948) where he says:

The Greeks along the Hellespont, on the contrary, were ruled by a satrap Mitrobates, who from Dascyleium on the south shore of the Propontus administered Hellespontine Phrygia or Tyaiy Drayahaa, "Those of the Sea."

This is generally true, except this is his citation from that claim, while very thorough, is just a list of Greek sources, none of which actually mention the Persian name. Every subsequent reference to Hellespontine Phrygia as Tyaiy Dryahaa, cites either this passage or a different text where the citations ultimately lead back to this passage. Olmstead's work has been popular for decades, very influential, and is available for free online. As such, several online sources I found quoted this sentence verbatim.

In reality, Tyaiy Dryahaa is only used twice in the entire Old Persian corpus, and is only used on its own once: In the Behistun Inscription of Darius the Great. It appears in the context of the earliest known list of lands (OP: dahyu) in the Persian Empire.

King Darius says: These are the countries which are subject unto me, and by the grace of Ahuramazda I became king of them: Persia, Elam, Babylonia, Assyria, Arabia, Egypt, the countries by the Sea {Tyaiy Dryahaa}, Lydia, the Greeks, Media, Armenia, Cappadocia, Parthia, Drangiana, Aria, Chorasmia, Bactria, Sogdia, Gandara, Scythia, Sattagydia, Arachosia and Maka; twenty-three lands in all. (DBa^(p) i.12-17)

Lists like this occur in several Achaemenid inscriptions in several languages, and are often shorthanded as lists of "satrapies." That's not really accurate. Nothing in any of these inscriptions actually associates these locations with specific governors, the satraps or xsaça-pā-van, in Persian. Many of them overlap broadly with the areas described by the Greeks and modern historians as "satrapies," but not all of them. For example, we know that there was not separate satrapy of "the Greeks." The Greeks in the empire fell under the jurisdiction of several different governors in their many settlements along the Mediterranean and Black Seas.

Likewise, later inscriptions like this list from the DNa inscritpion on the tomb of Darius the Great contain other examples. Nubia and the Libyans were underneath the Satrap of Egypt. Thrace was apparently under the Satrap of Hellespontine Phrygia. The Carians were included in Lydia. Likewise, the administrative archives from the Persian palace at Persepolis refer to a governor of Karmana, which is never listed in these lists of lands.

King Darius says: By the favor of Ahuramazda these are the countries which I seized outside of Persia; I ruled over them; they bore tribute to me; they did what was said to them by me; they held my law firmly; Media, Elam, Parthia, Aria, Bactria, Sogdia, Chorasmia, Drangiana, Arachosia, Sattagydia, Gandara, India, the haoma-drinking Scythians, the Scythians with pointed caps, Babylonia, Assyria, Arabia, Egypt, Armenia, Cappadocia, Lydia, the Greeks, the Scythians across the sea, Thrace, the sun hat-wearing Greeks, the Libyans, the Nubians, the men of Maka and the Carians. (DNa^(p) 15-30)

The conclusion of most historians today is that these lists, which only appear in the context of royal monuments, are not meant to convey administrative reality. Instead, they are intended to convey all of the major peoples and places under the kings' control.

This does leave people wondering what is meant by Tyaiy Dryahaa in the end. Evidently, it was part of how Darius the Great and his advisers thought about the empire around 520 BCE when the Behistun Inscription was created. But by the time Darius died in 486 BCE, it was no longer part of the list. Darius only ever expanded the empire, so either Tyaiy Dryahaa was no longer seen as important enough to include or the people and places included in "Those of the Sea," were redefined to fit some of the other groups listed in the DNa inscription.

Another of Darius' inscriptions might hold a clue. This is inscription DPe, from Persepolis, with most of the same list as Behistun (plus the addition of India) and this alteration:

the Greeks who are of the mainland and those who are by the sea, and those countries which are across the sea

In Old Persian:

Ya unâ tyaiy uškahyâ utâ tya iy dryahaâ utâ dahyâva t yâ para draya

I've bolded corresponding words to make things clearer without having to learn Old Persian.

In DPe, tyaiy dryahaa is clearly supposed to describe a subset of Greeks (OP: Yauna). In context, it seems like "those countries which are across the sea" is also supposed to describe the Greeks. Especially in that context, it seems likely that tyaiy dryahaa is intended to denote islanders. From the Persian perspective, Greek cities in Anatolia are the mainland, and Macedonia and the Greeks of Thrace were across the sea. That leaves the large number of Greek islands in the middle to be "those who are by the sea."

That may or may not be what was intended in the Behistun Inscription. In that original use, Tyaiy Dryahaa isn't specifically tied to the Greeks, so other interpretations abound. Hellespontine Phrygia is one option, but many important places "by the sea" don't have their own place in the Persian territory lists. Cyprus is another popular candidate, as are the various peoples of the Levantine coast. H.T. Wallinga suggested that it could refer to the region of Cyprus-Phoenicia-Cilicia on the basis that the area was the hub of the Achaemenid navy, but that importance developed only after Tyaiy Dryahaa fell out of use entirely.

Given the context of the DPe inscription, I think something linked to islands makes the most sense. That doesn't have to be limited to Greek islands or even just Mediterranean islands, but definitely some kind of islands.