In Odoo 17, you can override _compute_display_name​, to show customer name instead:

def _compute_display_name(self):
    for record in self:
        record.display_name = record.partner_id.name

Hi

Please try to inherit the project.task model, then you can add your own field on the calendar view

<record id="view_task_calendar" model="ir.ui.view">
<field name="name">project.task.calendar.view.calendar. inherit. module.name</field>
<field name="model">project.task</field>
<field name="inherit_id" ref="purchase.view_task_calendar"/>
      <field name="arch" type="XML">
<xpath expr="/calendar/field[@name='project_id']" position="after">
                        <field name="my_date"/>
                 </xpath>
      </field>
</record>

Hope it helps