Python

class ExtendPartner(models.Model):
    _inherit = 'res.partner'

    new_field = fields.Char(string='New field', required=True)

XML:
<odoo>
    <data>
        <record id="some_name" model="ir.ui.view">
            <field name="inherit_id" ref="<NAME OF THE PARTNER VIEW WHERE YOU WANT TO ADD>"/>
            <field model="res.partner"/>
            <field name="arch" type="xml">
                <xpath expr="expath expression to where position the new field" position="after">
                    <field name="new_field"/>
                </xpath>    
            </field>    
        </record>
    </data>
</odoo>

XML:

<field name="field_name" string="String" required="1"/>

Python:

name = fields.Char('Name', required=True,)

Dynamically on xml by conditions:

<field name="name"
        attrs="{'required': [(domain_condition)]}"/>

Add field on partner form

<record model="ir.ui.view" id="new_id">
    <field name="name">partner.view.name</field>
    <field name="model">res.partner</field>
    <field name="inherit_id" ref="base.view_partner_form" />
    <field name="priority" eval="20"/>
    <field name="arch" type="xml">
        <field name="desired_name" position="after">
            your code here
        </field>
    </field>

Note:- I can't comment on your post.

 name = fields.Char(
        string="Name",                   # Optional label of the field
        compute="_compute_name_custom",  # Transform the fields in computed fields
        store=True,                      # If computed it will store the result
        select=True,                     # Force index on field
        readonly=True,                   # Field will be readonly in views
        inverse="_write_name"            # On update trigger
        required=True,                   # Mandatory field
        translate=True,                  # Translation enable
        help='blabla',                   # Help tooltip text
        company_dependent=True,          # Transform columns to ir.property
        search='_search_function'        # Custom search function mainly used with compute
    )

   # The string key is not mandatory
   # by default it wil use the property name Capitalized

This is the verified code and works perfectly. You should search your code for other errors or paste your logs here.