I understand that today Easter is the holiday associated with the resurrection of Christ. But I have heard of a theory linking Easter with the Mesopotamian goddess of sex and fertility Ishtar (eggs and rabbits as symbols of fertility). This theory also states that with the rise of the Eastern Roman Empire the festival in celebration of Ishtar was changed to Easter. Does this theory have any evidence or historical records?
There is no evidence that Easter is linked to Ishtar, this is a false etymology. Here is a previous thread on the topic.
Side-note: In most Romance languages it is called some variant on pesach or passover; e.g. Pascua in Spanish or Italian, Paques in French, and so on. Also, Ishtar may be a sex goddess but she is very much not a fertility goddess in Mesopotamian tradition; Ishtar is emphatically a goddess of warfare, sexual lust, and in some ways the boundary between the netherworld and human world. There isn't really an exact "fertility goddess" in Mesopotamia, although various gods and goddesses take on that role at different times-Nisaba/Nidaba, Ninazu, and Nanna/Sin/Suen are all gods or goddesses who take on that role. In Anatolia and northern Syria the role of fertility goddess tended I think to be filled by Lelwanni, Hannahannah, and Kubaba.
This theory also states that with the rise of the Eastern Roman Empire the festival in celebration of Ishtar was changed to Easter.
The etymology of "Easter" actually derives from "Eostre", an Anglo-Saxon goddess of fertility and Spring.
The Anglo-Saxon historian Bede, writing in 725AD, describes this link in his book 'The Reckoning of Time':
Eosturmonath has a name which is now translated "Paschal month", and which was once called after a goddess of theirs named Eostre, in whose honour feasts were celebrated in that month. Now they designate that Paschal season by her name, calling the joys of the new rite by the time-honoured name of the old observance.
For context, the Paschal season Bede is referring to is what the Catholic Church currently calls "The fifty days from Easter Sunday to Pentecost".
However, in Bede's time:
The term Paschal Tide was usually interpreted to mean the two weeks between Palm and Low Sundays (Synod of Avignon, 1337); by St. Antonine of Florence it was restricted to Easter Sunday, Monday and Tuesday; by Angelo da Chiavasso it was defined as the period from Maundy Thursday to Low Sunday. Eugene IV, 8 July, 1440, authoritatively interpreted it to mean the two weeks between Palm and Low Sundays [G. Allmang, "Kölner Pastoralblatt" (Nov., 1910) 327 sq.].
Therefore, when Bede refers to the "Paschal month", he is talking about the month containing the two weeks centred on the Sunday that Jesus was reported to have risen from the dead, which became named after the Anglo-Saxon goddess Eostre.
The name doesn't come from Ishtar, it comes from Eostre.
The first record of Easter bunnies was in an 1682 essay by doctor Georg Franck von Franckenau, "De ovis paschalibus" where he describes it as a tradition of Alsace. It didn't become a general German and more international phenomenon until the 19th century.
Although the English name "Easter" probably derives from the Anglo-Saxon goddess "Eostre," the holiday itself is clearly Christian. Since at least the second century AD, it had been celebrated by the Christian church under the name "Pasche," derived from the name of the Jewish festival of Passover which was held to typify Jesus' sacrifice; that's still the name for Easter in many languages.