The word “Easter” is used in the Authorized Version of the Bible (KJV), but it is the result of poor translating from the Greek language in which the book of Acts was originally written. Other translations properly render the Greek word pascha as passover, not Easter.
Note what The Westminster Dictionary of the Bible has to say about this on page 145:
“Easter. Originally the spring festival in honor of the Teutonic goddess of light and spring known in Anglo-Saxon as Eastre. As early as the 8th century the name was transferred by the Anglo-Saxons to the Christian festival designed to celebrate the resurrection of Christ. In A.V. [Authorized Version] it occurs once (Acts 12:4), but is a MISTRANSLATION.”
Also notice the following from the Easton's Bible Dictionary, Thomas Nelson Publ.:
"EASTER - originally a Saxon word (Eostre), denoting a goddess of the Saxons, in honour of whom sacrifices were offered about the time of the Passover. Hence the name came to be given to the festival of the Resurrection of Christ, which occured at the time of the Passover. In the early English versions this word [Easter] was frequently used as the translation of the Greek pascha (the Passover). When the Authorized Version [KJV] (1611) was formed, the word `passover' was used in all passages in which this word pascha occurred, except in Acts 12:4. In the Revised Version the proper word, "passover," is always used."
For much more concerning Easter, see:
Why Don't Jehovah's Witnesses Celebrate Easter? (Defend Jehovah's Witnesses)