Hi,

display_name is computed from the name_get function of the model,

@api.depends(lambda self: (self._rec_name,) if self._rec_name else ())
def _compute_display_name(self):
    """Compute the value of the `display_name` field.

    In general `display_name` is equal to calling `name_get()[0][1]`.

    In that case, it is recommended to use `display_name` to uniformize the
    code and to potentially take advantage of prefetch when applicable.

    However some models might override this method. For them, the behavior
    might differ, and it is important to select which of `display_name` or
    `name_get()[0][1]` to call depending on the desired result.
    """
    names = dict(self.name_get())
    for record in self:
        record.display_name = names.get(record.id, False)

if the name_get function is override in the model, it will be taking the given rec_name for the model, and if the rec_name is not set, it will take the name field value in the model.

Reference:

1. Use of Name Get Function in Odoo

2. What is rec name for Models in Odoo Development

Thanks