I cant find an answer to this with some basic research or on r/AskHistorians. I assume there must be some oldest text that names the day of the week. Has there ever been a competing system like Babylonians saying it's Monday while Egyptians said it was Wednesday?
The words we use today for the days of the week come from Old English, a language in the West Germanic Language group. Here is a list of the modern names, their root names and their meaning.
-Monday; Mōnandæg, Day of the Moon.
-Tuesday; Tīwesdæg, Day of Tiw. A Germanic god of war and the sky. Think Týr from Old Norse or Mars from the Romans.
-Wednesday; Wōdnesdæg, Day of Odin.
-Thursday; Thunresdæg, Day of Thunder, sometimes Day of Thor.
-Friday; Frīgedæg, Day of Frigga, Odin’s wife Frigg.
-Saturday, Sæternesdæg, Day of Saturn, Old English word but a Roman god of agriculture.
-Sunday; Sunnandæg, Day of the Sun.
Old English lasted in Britain from about 450AD to 1150AD a period of about 700 years.
In between the 1st and 3rd centuries(0-300AD) the Romans were transitioning from an 8-day weekly cycle to a 7-day cycle.
In the 7th century BC the Babylonians were naming days after celestial bodies and making up for calendar errors by occasionally switching to 8 or 9 day weeks. Their calendar system was based off one from the Sumerians. I think it’s safe to say humans have been naming the days of the week since the discovery of agriculture, when keeping track of passed time became essential.
I hope I could answer at least part of your question.