As adjunct faculty at four-year university, with no PhD, what should I have my students call me?
To a fairly large extent this can be student driven, actually. The students get into habits of speech. Some places it results in fairly formal address, in which case "Professor" would be fine in the US. Other places it is common to use first names. Your colleagues should be able to tell you the local custom. 

In the US, "Professor" has both a generic and a technical sense. Students normally use it as a generic term. Undergraduates, at least. There are some places in which you are Doctor if you have a doctorate and Professor otherwise. Not especially consistent, but as the kids say, "whatever". 

There are a few places that impose formal rules, but you'd have been informed of that if it were the case. But, no matter your wishes, the students will likely do what they do. 

I once tried to impose "first names only" rules on a set of doctoral students. Some went along ok, but others couldn't make the jump. I was, forever, Professor Buffy to them. 

If, on the first day of class, you write your name on the board as "Professor MathStudent1324", most will go along. And if you write "Maria MathStudent1324" you will probably wind up as Maria. But like I said, they will do what feels comfortable to them.