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Kind of. To the extent that Europeans were even aware that a body of water existed beyond China, it was indeed thought to be connected to the Atlantic. But this body of water was often given its own name nonetheless.
Prior to the Age of Exploration, classical geography dominated European views of the world. Ancient Greeks already had a concept of a World Ocean; in Homeric terms this was expressed as a river around the world.
Homeric view of the world, depicting the Ocean River surrounding all lands.
Herodotus wrote for instance:
For that on which the Greeks sail, and the sea beyond the pillars of Heracles, which they call Atlantic, and the Red Sea, are all one
Hdt. 1.202.4
This world encircling sea was often called Ocean. Importantly, some authors also applied the specific names given to the Atlantic to the entire body of water. Cicero, for example, wrote that:
For all of the earth with which you have any concern . . . is a mere little island, surrounded by that sea which you on earth call the Atlantic, the Great Sea, the Ocean.
Cic. Rep. 6.20
So yes, in this sense, they were calling the Pacific Atlantic.
However, just because the ocean is connected, doesn't mean that individual parts weren't given their own names. In the Herodotus example above, the Red Sea was acknowledged to be linked to the Atlantic, but still given its own names.
Accordingly, some writers also gave specific names to the sea beyond China. Pliny for instance names the Eastern Ocean after Serica, which is usually identified as North China. It is certainly considered to be the extreme end of the earth.
Aggripa bounds the Caspian Sea and the nations around it, including Armenia, on the east by the Ocean of the Seres.
Mela likewise places an ocean off the Seres on the end of Asia, which he called Eous Oceanus. His De situ orbis libri III remained in use in Europe until the 16th century.