Someone who is not on the board objected to someone's use of the term Sunday in common discussion here. In response I thought I'd post what James Durham has to say as far as the parameters on this. I think we should use the Scripture given name Lord's Day amongst the community of believers. Sunday may be used in a civil and otherwise pagan and unbelieving context. See Durham's comments below, from his Commentary on Revelation, chapter one, lecture four. Note that as much as there is a given name in Scripture for the first day of the week, there is also a broader principle from approved example of speaking in a culture so as to be understood.
...II. The name that the Lord’s Day gets....
II. For the second, seeing it gets this name to be called the Lord’s day, it may be questioned here concerning our manner of speaking of days, calling the Lord’s Day Sunday, the next day after it Monday, etc., which has the first rise from superstition, if not from idolatry, some of them being attributed to planets, as Sunday and Monday; some of them to idols, as Thursday, etc. But to speak to the thing itself, look to the primitive times, we will find Sunday called the Lord’s Day, and the days of the week by the first, second, third, etc. But the names of days, being like the names of places and months, folks must speak of them as they are in use, and scripture warrants us so to do. Acts 17:22, Paul is said to stand in the midst of Mars hill. Acts 28:11 speaks of a ship, whose sign was Castor and Pollux. So, March, January, July and August, are from the idols Mars and Janus, or derived from men that appropriate more than ordinary to themselves. And though it was ordinary to Christians in the primitive times to call this day the Lord’s day among themselves, yet when they had dealing with the Jews, they called it the Sabbath, and when they had dealing with the heathen, they called it the Sunday. And so, though it be best to speak of days as scripture names them, yet it is agreeable with scripture to design or denominate them as they are in use among a people, especially where no superstitious use is in naming of them.
II. For the second, seeing it gets this name to be called the Lord’s day, it may be questioned here concerning our manner of speaking of days, calling the Lord’s Day Sunday, the next day after it Monday, etc., which has the first rise from superstition, if not from idolatry, some of them being attributed to planets, as Sunday and Monday; some of them to idols, as Thursday, etc. But to speak to the thing itself, look to the primitive times, we will find Sunday called the Lord’s Day, and the days of the week by the first, second, third, etc. But the names of days, being like the names of places and months, folks must speak of them as they are in use, and scripture warrants us so to do. Acts 17:22, Paul is said to stand in the midst of Mars hill. Acts 28:11 speaks of a ship, whose sign was Castor and Pollux. So, March, January, July and August, are from the idols Mars and Janus, or derived from men that appropriate more than ordinary to themselves. And though it was ordinary to Christians in the primitive times to call this day the Lord’s day among themselves, yet when they had dealing with the Jews, they called it the Sabbath, and when they had dealing with the heathen, they called it the Sunday. And so, though it be best to speak of days as scripture names them, yet it is agreeable with scripture to design or denominate them as they are in use among a people, especially where no superstitious use is in naming of them.