What is the scientific name of this flying insect?
This insect is, indeed, related to dragonflies. This is a damselfly.

Damselflies are Odonata insects from the Suborder Zygoptera. Unlike dragonflies (Suborder Anisoptera), damselflies fold their wings when resting. This is the most noticeable difference between damselflies and dragonflies:



Regarding your specimen, I'd say that it is Caconeura ramburi, the indian blue bambootail. Here is an image for comparison:



The site where I found that image, conveniently called Odonata of India, is a good source of information.