Christianity Today excerpts from Sunday: A History of the First Day from Babylonia to the Superbowl, by Craig Harline. Apparently, when it became common for Christians to worship on the first day of the week they called it "The Lord's Day," to distinguish their practice from that of the pagans, but the time came when "Sunday" was the acceptable name for the day. Two paragraphs:
Most telling here is that even the Sun, greatest symbol of Roman paganism, no longer had exclusively pagan meaning. Some early Christians had already used, with mixed results, the Sun's imagery to speak of Christ. But such imagery became more acceptable during the fourth century, when far more Christians began calling the first day "Sunday" rather than exclusively the Lord's Day—despite even the condemnations of an Augustine or a Chrysostom. Saint Jerome himself defended the practice, saying, why shouldn't we call it Sunday, since Christ is the Sun of justice and has filled the world with his light? Jerome even claimed that Sunday took its name from Christ the Sun rather than from the physical Sun. This was a classic example of reading present desires into the past, but Jerome demonstrated perfectly the ability to take something previously seen as Roman and make it Christian. ....The Son's Day to Sunday | Christianity Today | A Magazine of Evangelical Conviction
In sum, by 600 one may speak of a Christian Sunday in the old Roman provinces touching the Mediterranean. By 800 this had expanded into the large portions of northern Europe already Christianized. Like the Jewish Sabbath, Sunday had become the most important day of the week, indeed gave the week most of its meaning. Once thoroughly pagan, Sunday now had a decidedly Christian connotation. It would remain this way for so long that countless generations in the Western world would consider the day's very existence, name, and status as obvious, unquestioned facts of life, as if things had always been this way.