Is it permissible to wear clothes bearing the Lacoste crocodile logo and to liken oneself to it? And is the prayer valid while wearing such clothes?

Prayer performed while wearing clothes that have images on them is valid. However, if the images are clear in their features, it is not permissible to wear them, and the person who wears them incurs sin, even though their prayer is valid. But if the image is small and its features are not clear, then there is no harm in that.