You can change this by drilling down to the details of the contact by selecting the contact and clicking the Details button (the blue arrow in a box). This will take you to the Account Contact screen where you can enter the Contact Role.

Thanks ! 
 

Could you attach a screen?

Do you mean to connect the contact to the Customer in Person window (‘Contact for Customer’)  and the Contact information as below?

I am looking for an option where I do not need to connect the contact added to the customer but add the contact with Role information. 

Any help would be appreciated. 

I am talking about this option.