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Passage is at the southern-most narrow point on the Suir Estuary. Meaning it has long been the point of a ferry crossing. Hence a passage or crossing-point. (See the 6 inch 1830s OSI map for example.)
Passage/Pasáiste derives ultimately from the Latin passagium. Which means "ferry". Other sources suggest that pasáiste (in Munster Irish) was used to imply a "place one can swim across". (See Power's 1907 "Placenames of Decies (Waterford)" for example. The updated version of which covers both the Latin and Irish derivations. Search "passagium" in the PDF version.)
Passage is made up of two townlands. Passage East and Passage West. Ultimately the town took the name "Passage East". Possibly to differentiate it from Passage West in County Cork. Passage West is also at a narrow point in a river channel. And also a historic crossing/passage point. (See Lewis's 1837 "Topographical Dictionary of Ireland" for example. Which lists "Passage (East)" in Waterford and "Passage (West)" in Cork.)
In short, it was called "Passage" because it is a "passage point" across the river. It is referred to as "Passage East" to differentiate it from other places called "Passage" in the region (which are also passage points across rivers).