With respect John, calling it Finance, which originally started in the UK in US owned UK companies then US-dominated industries , has become more widespread but is absolutely still not universal. And does not change the fact that what Accounts Departments do is pretty much the same thing as people in Finance Departments do until you get to a very high level.
Thoigh I will agree with you that most large companies call the function Finance these days. An “Accoints Department” referred to by a country solicitor, say, might be as little as a part-time person doing only a day or two a week.
And as we are talking smaller businesses that are more likely to be using the “Accounts Department” naming and as for bigger businesses calling it an “Accounts Department” was indeed long ago, of course calling Mrs Rachel Reeves “Rachel from Accounts’ has several further layers of insult brought in by …from Accounts”. As well as belittling her and making her sound junior by using her first name.
Don’t get me wrong I actually found it witty myself but let’s not refrain from unpacking all the levels of insult here. There are quite a few and these particular insults would not be tried on a man, as they reflect real female work history.