What is the name of cookie that has a base marshmallow and coloured coconut looks like flower?

You're likely thinking of Coconut Macaroons.

Coconut macaroons are small, sweet cookies made with shredded coconut, egg whites, and sugar. They are often shaped into small mounds, and the shredded coconut is often colored to resemble flower petals. While not a traditional marshmallow base, the texture of the macaroon can be soft and chewy, similar to a marshmallow.

Let me know if that's what you were looking for!