The land that we know today as Israel/Palestine has undergone several names throughout the centuries. It seems that the quote you have given comes from a pro-Arab anti-Zionism source. I will try to avoid discussing the current Israeli-Palestinian conflict, as there are books upon books of debate over whether the current people living in Israel are "true Israelis" or who the land "rightfully belongs to" I will focus more instead on the names the land have gone through during its history. Keep in mind that I know more about ancient Israel from Biblical times to the time of the Maccabees than I do from the time of the Roman occupation to the present day, so my answer will be more prone to error as the timeline progresses. The question on general information on the Philistines as a people Has been answered before, Lastly, I will use "Canaan" as a generic term for the land to avoid biases

Some of the names of Canaan were given by the people occupying the land, while others were given either by outside observers, or by more powerful, ruling empires.

Canaan: The word "Canaanite" is used to describe the people that lived and dominated in Canaan before the establishment of the Israelites within Canaan, the word "Canaan" dates from at least the time of the Amarna Period during the reign of the Pharaoh Akhenaten in the 14th century BC.

Israel: This is perhaps the most well-known name of the land, since it shares the name with the current United Nations recognized country which occupies much of the land. It is one of the most ancient names of Canaan, with the earliest agreed upon reference of the name "Israel" belonging to the Egyptian Merneptah Stele, from c. 1209 BC. The Stele is named as such as it was likely written during the time of the Pharaoh Merneptah, the Stele brags about Merneptah's achievements, including laying waste to a group of people referred to as "Israel" "Israel is wasted, its seed is not" (Locatell). According to Biblical chronology and our understanding of ancient Israel, 1209 BC would have preceded the Kingdom of Israel, as such, the name "Israel" in this case more likely refers to a group of people rather than a nation.

One of the earliest non-Biblical sources referencing Israel as a nation comes from the Mesha Stele from c. 850 BC, it chronicles a battle between Mesha, the king of Moab, and Omri, the king of Israel. The Stele also contains the earliest non-Biblical reference to the Israelite god YHWH, who would be worshiped by today's Jews, Christians, and Muslims (NewWorldEncyclopedia) The Biblical account states that the Israelites, led by Joshua, successor of Moses, took the land from the Canaanites by force, burning several of their cities in the process, contemporary archaeological evidence suggests the transition of rule from the Canaanites to the Israelites was much more gradual, and that the Canaanites rather peacefully integrated with the Israelites over the span of centuries (Hasson).

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Judah and its Variants: The name "Judah" referred originally to one of the tribes of Israel, which became the Kingdom of Judah, south of Israel. The name Judah would become especially popular following the Babylonian Exile (the word "Judaism" literally means "the way of the people of Judah") (Gilad). Judah would be the name given to the land by the Persians, the Hasmonean Dynasty (that is, Judea under the Maccabees) and the Romans before the time of Hadrian.

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Philistia and its variants (including Palestine): The name "Philistia" is used several times throughout the Hebrew Bible (i.e the Old Testament) to describe the collection of cities inhabited by the Philistines; the name "Palestine" is likely derived from Philistia. Though the word "Palestine" is never explicitly mentioned in the Bible, there are ancient sources that refer to the name as such. The earliest reference we have to the name comes from the Greek historian Herodotus, in his work The Histories which was written in the 5th century BC. Herodotus mentions a group of people known as the Palestinians (Greek: Παλαιστίνων) who practice circumcision (Herodotus 2:104). Up until the time of the Romans, however, "Palestine" was a generic term to describe the land of Canaan, as the land would have been subjected by the Persians during the time of Herodotus, the Persian name for the land was "Yehud" (i.e Judea) The name "Palestine" would be the official name given to them by the Roman Emperor Hadrian following the Jewish-Roman Wars as a punishment for the Jewish rebellion, he wanted to give them a name that resembled the name of their enemies (the Philistines) (Latin: Syria Palestina, which you mentioned earlier) (Mark). The implication that the concept of Palestine arose during or after Ottoman Rule is false.

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The land of Canaan under the Ottoman Empire would be counted as part of the Ottoman territory of Syria, and the name Palestine would be reintroduced during the British occupation of Palestine in 1923 as the "British Mandate of Palestine" (Ginat)

There is also the name "Zion" which wasn't an official name used to describe Canaan, but the Hebrew Bible uses it as a spiritual term as a synonym for Jerusalem, and Israel in general (hence the belief in the necessity of the modern State of Israel being known as Zionism) Additionally, there were other lands around Israel and Judah, such as Edom, Moab, Aram-Damascus, and Ammon.

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Due to the countless times Canaan has been occupied by a variety of peoples, and events such as the Diaspora of the Jews by the Romans following the Jewish-Roman Wars, it is practically futile to determine who the land of Israel/Palestine currently belongs to, as so many groups of people can claim the land to be their land, and they would all have genuine reasons as to why.

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I hope my answer helped you in some way!

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Sources

"Mesha Stele.” Mesha Stele - New World Encyclopedia, 18 Sept. 2018, https://www.newworldencyclopedia.org/entry/Mesha_Stele.

Gilad, Elon, et al. “Why Are Jews Called Jews?” Haaretz.com, 15 Feb. 2017, https://www.haaretz.com/archaeology/why-are-jews-called-jews-1.5410757.

Ginat, Avital. “British Mandate for Palestine.” New Articles RSS, 7 Dec. 2018, https://encyclopedia.1914-1918-online.net/article/british_mandate_for_palestine.

Hasson, Nir. “Is the Bible a True Story? Recent Finds and Technological Advances Yield Surprising Discoveries: Special Report.” Haaretz.com, 1 Nov. 2017, https://www.haaretz.com/archaeology/MAGAZINE-is-the-bible-a-true-story-latest-archaeological-finds-yield-surprises-1.5626647.

Locatell. “‘Merneptah Stele’, in J. D. Barry Et Al (Eds.), The Lexham Bible Dictionary. Bellingham, WA: Lexham Press, 2015.” Lexham Bible Dictionary, 2015, https://www.academia.edu/16568997/_Merneptah_Stele_in_J._D._Barry_et_al_eds._The_Lexham_Bible_Dictionary._Bellingham_WA_Lexham_Press_2015.

Mark, Joshua J. “Palestine.” Ancient History Encyclopedia, Ancient History Encyclopedia, 11 Nov. 2019, https://www.ancient.eu/palestine/.