Christians in the first century A.D. did not celebrate anything called Easter. The word “Easter” (which many sources say is derived from the false fertility goddess Ishtar / Ashtoreth / Astarte / Eostre / Eastre, depending on the source) in Acts 12:4 of the KJV is a disappointing translation of the original word “pascha,” meaning Passover. Passover was not the day Jesus was resurrected, but the night they took Him to be slain (Matt. 26:17-ff; cf. Ex. 12:1-6). It was not the early Christians celebrating the Passover in Acts 12, but the enemies of Christianity–Herod and the Jews who were killing Christians (12:1-4). Early Christians were gathering weekly to remember the Lord’s death, burial, and resurrection on the first day of every week, the day Jesus arose from the grave, and so should we, after we have obeyed the pure Gospel of Christ (Mk. 16:9, 15, 16; Jn. 4:23, 24; Acts 2:36-42; 20:6, 7; 1 Cor. 11:20; cf. 16:2; 2 Thess. 1:7-9; 2:15).
There is some debate about the origins of the name “Easter,” but no matter what it is called, there is no Scriptural evidence that the first century church observed it. If the name is truly derived from a pagan goddess, then whenever someone says “Easter,” he is saying the name of a false goddess that should have been forsaken and forgotten a long time ago (Hos. 2:17), but may we remember our Lord in the way He desires always! (Ex. 23:13; Deut. 12:3; Josh. 23:7; 1 Cor. 11:25).