mongoose for if-else kind of query with find()

I have a db collection where I need to write if/else kind of query with string datatype. Tried with $cond and $switch but they don't seem to be working.

Requirement is:

{
    {
     name: 'xyz',
     state: 'ABC'
    },
    {
     name: 'abc',
     state: 'XYZ'
    },
    {
     name: 'xyz',
     state: 'ABC'
    },
    {
     name: 'mno',
     state: 'MNO'
    }
}

I need to write condition if user name is 'xyz' then and then only state should be used for searching else not.