Ykhjuy

I will be teaching at a four year university as adjunct faculty. Is it okay to have my students to call me Professor LastName, even if I do not have this title formally? If not, what other options do I have? I quite dislike Ms.. At my old college, I had my students call me by my first name, but instead I got a strange combination of "Teacher" and "Ms. FirstName" and "Miss FirstName" which makes me feel like a kindergarten teacher.

(Note: I have seen this question asked in a variety of ways but not in the case where the asker does not have a PhD.)

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.

Professor 1234 is the proper greeting. You don't need to be permanent faculty or have a Ph.D. to get this title when in class and doing the work of a professor.

One of my colleagues was called Doctor R by the students and he was happy, while they avoided the formality of his family name but showed sufficient respect. Honour on both sides then...

I have to add a bit of local flavour to the answers: Whilst in some countries "professor" is just a job title, in others it is an academic title which may not be used unless you earned it. E.g. in Germany it could result in up to a year of prison (see https://dejure.org/gesetze/StGB/132a.html).
Therefore, in Germany you should not give yourself a title (neither "Dr." nor "Professor") unless you are holding the title.