I want to see the domain name in the logical diagram instead of the datatype. How can I do it?

Go to Design Properties (either double-click the design name or right-click and select Properties). Go to Settings, Diagram, Logical Model and select Domain Name for the Domain presentation:

domainname

 

See the datatype for Name before the change (Used Logical Type selected):

dom1

 

And after we changed the Domain presentation to Domain Name (the domain used for the attribute Name is called NameDomain in our example):

dom2