No, it isn't a religion. Yoga is a system of harmonious self-exploration. People of different religious views, as well as people without relation to any religion can practice do yoga.
Although sometimes there are some terms and explanations in yoga that sound similar to the religious ones, for example, the names of some poses, but it's just a tribute to the tradition and cultural mentality of those people where yoga was preserved. If yoga had been preserved in other country, then we would probably have had characters related to that nation and their lifestyle.
It should also be remembered that the uncritical use of names and terms of Hindu mythology thoroughly permeates in the daily life of ordinary people, scientists, cultural figures and politicians. This is a distinctive characteristic of eastern people, who have given us some parts of yoga. Therefore it would be wise to see these religious characters and terms just in the same way as Ancient Greek myths were used in the European science.