I am current studying a Ph.D. program with scholarship and applying for another university to restart my Ph.D. candidature. In terms of positively earning the new offer, the scholarship in next university is also the key concern before the prospective enrollment. In fact, the scholarship I have now is a university basis and can sponsor me for three years in total. Becuase of the problem with the supervisor, I have to take an action to transfer. 

My Ph.D. colleagues said that my situation might cause a difficulty in receiving the full scholarship again from the scholarship office of the new university. Her main point is that I did not completely use the full scholarship at this stage and discontinue the program voluntarily. The scholarship office might suspect my future academic performance if drop the study again. So, I think a simple way to avoid this embarrassing history is to obscure the reality I am taking a scholarship for higher likelihoods to new scholarship. But I have an alternative thought: the achievement of scholarship attained is an evidence that other organization or department believes my academic potential. The awards will attract more award, so I should bravely put the record of Ph.D. scholarship award on my CV to the application. 

In my scenario, the first Ph.D. program with full scholarship is a stigma as my colleagues thought, or an honor to convince the scholarship office of the new university to award my new Ph.D. program by the other funding sources' encouragement? Please give me your thought to help me to mold my CV, thank you!

You need to be honest - there's no point in hiding that you have already started a PhD and are looking to quit that and start another. Academia is a small place and people talk. If you don't tell them and they find out, it will look like you were being deliberately dishonest.

But do you need to do this at all? Can't you just see if you can transfer supervisor in your current institution?

Also, depending on the funding source you may not even be eligible for a second set of funding as you have already received funding. If you were to present yourself as having not done a PhD before, or as having not received funding, then you are potentially committing fraud.