Should I mention not completing a Phd in a cover letter? I am possibly quitting my PhD. I am 2 years into my PhD and now I am writing a cover letter for an opening at a company. My question is, do I mention in the cover letter why I am quitting ? In my CV I just mention what I've done for the past two years and write that the PhD is not complete. 

I feel like I need to mention it, because it feels like an elephant in the room. Also to avoid confusion I think I need to mention it. (e.g. They can think I tend to continue working on the PhD while I want to work there).
Yes. They are going to see it in your CV anyway and if you say nothing, it just looks like you are trying to hide something and they are going to assume the worst. I would tell them the reasons why I quit (e.g. what to do something applied, ...).