What is the name given to religions which were present in various societies around the world

before western expansion?

Animistic religions.

Explanation:

They worshipped forces of nature - the sun, the moon, the wind, etc. - and also believed in spirits. There are still animistic religions in the world just like shinto in Japan, whose practice is combined with Buddhism. Also the practice of Taoism in China and Taiwan shows some elements of animism.