This is a difficult one! At first I thought it doesn't matter - what is most important is that they all have the same main goal of being more sustainable and more ecologically friendly. However, having set criteria does make it easier to monitor the success of different cities and compare and contrast their progress. In general, being able to measure/monitor something against set goals makes it more likely that the goals will be achieved - so perhaps it is important to have international standards for eco-cities. It might also make it easier for new cities that want to become eco-cities to know what they need to achieve and make planning easier.
I also think having a common name might be important, as it can form a 'brand' or 'big idea' for people to rally around. When there is a common term for something people find it easier to discuss and it more easily becomes accepted as a real 'thing'.