Globalisation is a very contentious subject and has invited strong criticism all over the globe. Critics of globalisation make a variety of arguments. Those on the left argue that contemporary globalisation represents a particular phase of global capitalism that makes the rich richer (and fewer) and the poor poorer. The weakening of the state leads to a reduction in the capacity of the state to protect the interest of its poor.

What is the name of the process where each culture starts becoming more different and distinctive?

Cultural heterogenization.

While cultural homogenization is an aspect of globalisation, the same process also generates precisely the opposite effect. It leads to each culture becoming more different and distinctive.  This phenomenon is called cultural heterogenization. This is not to deny that there remain differences in power when cultures interact but instead more fundamentally to suggest that cultural exchange is rarely one way.