I have done a research paper with someone in industry, while doing a Phd. Is it important to include my supervisor name also in research paper. Will three names be a good thing or should i go with 2 names.
Authorship should be decided by who made intellectual contributions to the work, not by feelings that three is or is not a better number than two.
The Vancouver Protocol is generally considered as the authoritative guideline for ethics in science publishing. Here it is stated:
"Authorship should be limited to those who have made a significant contribution to the concept, design, execution or interpretation of the research study. All those who have made significant contributions should be offered the opportunity to be listed as authors. Other individuals who have contributed to the study should be acknowledged, but not identified as authors. The sources of financial support for the project should be disclosed."
If your supervisor did not make any contribution, she should not be included on the author list.
If your supervisor made a significant contribution, she should be offered authorship.
There is clearly a middle category here. In my field it is usually considered "nice" to offer a contributor who have made a contribution bordering significant, a chance to contribute enough to warrant authorship before the project is finished.
In any case, you should discuss the matter with your supervisor before publishing. You also ought to investigate whether your university has a course on publishing ethics, and consider taking it.