When someone asks our name, we use I am [name]. Also, we use I am to express our feelings, like I am sorry, and I am happy. So do we use I am for both our identity and our feelings?
Yes. Unlike some other languages (eg Spanish, Japanese), English uses the same copula be for contingent properties, innate properties, identity, and sometimes location:
I am happy (contingent or transitory property)
I am human (innate or permanent property)
I am Colin (identity)
I am in my house (location).