It was in the 3rd year of Meiji that the family name was changed to Saga.

Literal

Family-name [object-を] Saga [into-と] changed-surname [nominalizer-の] [topic-は] Meiji 3-year was.

A historical/genealogical note. 家名 ('family name,' 'house name') is a slightly formal word for a surname, especially in the context of family lineage and historical records. 改姓する ('to change one's surname,' 'to adopt a new family name') is a legal/administrative verb. The construction ~のは~でした is the cleft focusing on the time: 'it was in Meiji 3 that...' Note the era-based dating: 明治3年 ('Meiji 3') = 1870 in the Gregorian calendar. Japanese still uses era-based dates alongside Western dates, especially in legal, historical, and genealogical contexts.