Naming Duos: Why "Hall and Oates" over "Oates and Hall"?

I don't think you're going to find one definitive answer.

Some combinations of words "sound better" because of their stress rhythm.

Some are easier to say because of the amount you have to move your mouth (this is called something, but it's been a while since I was an English major). In other words "Hall and Oates" is easier to say because your mouth doesn't have to move much from the "l" in "Hall" to the "a" in "and", or from the "d" in "and" to the "O" in "Oates". Compare that to "Oates and Hall" by thinking about how much your mouth has to move from the "s" in "Oates" to the "a" in "and", or from the "d" in "and" to the "H" in "Hall".

Others sound better because you're just used to them being said that way: I would argue that "Kel and Kenan" is easier to say (judging by the mouth-movement measure), but it "sounds better" as "Kenan and Kel" simply because that's what I grew up hearing. I wouldn't be surprised if they chose the "harder to say" version because it also might be more fun to say, but that's just guessing.

So there is no rule saying which combination sounds better, or is easier to say. There's also no rule saying that everybody should go for the combination that sounds better or is easier to say. It's going to depend entirely on your context.

I would further argue that it doesn't really matter in your case. Both "Milkshakes and Manhattans" and "Manhattans and Milkshakes" have similar stress rhythms and "mouth movement distance". Go with whatever sounds best to you, because I promise nobody else is worrying about it as much as you are.