Yoga is no religion
Yoga is not a religion and it has never been. Still, yoga is often practices by religious people and some of the traditional yogic forms involve steps related to religion. Yoga is at least traditionally most often related to Hinduism, which is one of the major religions of the world. Still Hinduism is not a religion as that concept is most often understood in the western, Christian world. Hinduism is not a set of dogmas regarding God and man and the relationship between the two, which every member of Hinduism is supposed to declare that they believe in. Rather Hinduism is a collective name of a lot of diverse forms of religious practices and thinking, traditionally mostly within the borders of India. In this area, religion is most often considered a private affair between every human and his/her God.
Yoga, on the other hand, is a kind of practical spiritual science that has been practiced in India but also in other parts of the world since ancient times. Yoga is most often not strongly connected to any specific religious beliefs. Thus, as a yogic practitioner, you are not normally expected to believe anything specific, or to declare your beliefs in any formal way. Nor are such beliefs normally a condition for benefitting from yogic practices. People from all religions can benefit from the practices of yoga.
When it comes to yogic texts, they are of course written by people with a variety of different religious and other beliefs. And of course some of those texts are influenced by the author’s beliefs. However, this doesn’t turn yoga into a religious belief more than it does with any other subject. There are different views on yoga, of course, and some of them are religiously inspired, but this is often the case in science of any kind.
The traditional yogic philosophy is also often connected to traditional Indian philosophy, which may be influenced by Hinduism. If so, this may also have influenced some yogic exercises, so that texts or words, such as the names of Gods and Goddesses, are used as mantras in yogic practices. However, most yogic practices do not involve the use of mantras with a spiritual meaning or other spiritual words or texts. And the use of such doesn’t normally mean that the religious quality of the word is considered of importance for the benefits of the yogic practices. On the contrary, the choice of words is more often based on the qualities of the sounds.
If you still feel you need to exclude everything that has any religious meaning in any religion connected to the yogic tradition in question from your yogic practices, this is probably rather easy to do.