co-authorship of the unresponsive and careless advisor? My paper, that is part of my thesis, has been accepted to a conference as a part of the poster session. In the paper, I have mentioned my gratitutes to my supervisors. In fact, an unofficial supervisor of mine who works at the same place with me, acted and helped me more than my actual supervisor deserves all the credits in this thesis. (My main supervisor lives in another city so that we met only 2-3 times, but the unofficial supervisor I mentioned helped me enormously as my official one advised me to work with her, no need to mention, she's not a faculty member but holds an associate professorship..) So it's a basically an unresponsive thesis advisor issue.

In the submission of my final version of the thesis for the conference, I want to make her my co-author if she accepts. 
But as there is literally no input from my actual supervisor, I do not want to put his name. (He also said to me once that you made all the work by yourself without me or if she (the 2nd person I work on my thesis, who is not officially assigned for my advisorship) accepts what you did then I'm fine, so he does not care at all what's going on such that I doubt if he reads the final draft of the work I sent.

So would it be okay to not to include his name?
What do you suggest?
thanks in advance!
This is a common dilemma in academia that can quickly escalate to sorrow. My advice is short and straightforward: once the manuscript is ready from your side, politely approach your both supervisors and ask them directly about their expectations concerning authorship.
I understand the situation may feel uncomfortable and you'd prefer to make this decision relying on everyone's best judgement, but most of the times supervisors are overly touchy regarding merit and authorships. 

Thread carefully there and be frank with your superiors. Good luck!