Can I still participate in conferences, while I'm no longer an academic student? Can I still participate in conferences and use the university name, while I'm no longer an academic student at the university?

As I could not complete the study, but I'm still interested in my unfinished research and want to continue it somehow! is it possible to use my university name in the paper?
First part of the question: 

unless specifically stated by conference organisers, nothing prevents anyone without specific higher education affiliation to contribute to conferences. 

If organisers want to know more about your situation as they review paper submissions, they can always get in touch with you before they shortlist selected papers.

Second part of the question:

Your study circumstances are not relevant to assess the quality of your potential conference contribution.

Maybe it depends on your academic field, however there are many conferences where you can see individuals who contribute or a poster who are listed as 'independent' or 'independent researcher'. Just serves to show that quality research is not conditioned by any institutional affiliation. 

Using the name of a university you are not affiliated with in any role is a deception. You should not feel compelled that you have to have your name coming with a university's name to increase the potential for your paper proposal to be accepted.