Is it possible to define equality for named types/structs?

No. You can't modify the equality operator and there is no built-in way to add support for custom types to use == syntax. Instead you should compare the pointer values using reflect.DeepEqual.

Go supports equality checking structs.

type Person struct {
    Name string
}

a := Person{"Bill DeRose"}
b := Person{"Bill DeRose"}

a == b // true

It won't work with pointer fields (in the way you want) because the pointer addresses are different.

type Person struct {
    Friend *Person
}

a := Person{Friend: &Person{}}
b := Person{Friend: &Person{}}

a == b // false


import "reflect"

a := Person{Friend: &Person{}}
b := Person{Friend: &Person{}}

reflect.DeepEqual(a, b) // true

Keep in mind there are caveats.

In general DeepEqual is a recursive relaxation of Go's == operator. However, this idea is impossible to implement without some inconsistency. Specifically, it is possible for a value to be unequal to itself, either because it is of func type (uncomparable in general) or because it is a floating-point NaN value (not equal to itself in floating-point comparison), or because it is an array, struct, or interface containing such a value.

No, this is not user-definable. Go has strict rules what counts as equal, and even what is comparable which itself is based on assignability. Take a look at the Comparison operators section of the spec.