<?xml version="1.0" encoding="UTF-8" ?>
<odoo>
    <record id="view_partner_form" model="ir.ui.view">
        <field name="name">res.partner.form</field>
        <field name="model">res.partner</field>
        <field name="inherit_id" ref="base.view_partner_form" />
        <field name="arch" type="xml">
            <field name="vat" position="before">
                <field
                    name="company_group_id"
                    attrs="{'invisible': [('is_company','=', False)]}"
                />
            </field>
        </field>
    </record>
    <record id="view_res_partner_filter" model="ir.ui.view">
        <field name="name">res.partner.select</field>
        <field name="model">res.partner</field>
        <field name="inherit_id" ref="base.view_res_partner_filter" />
        <field name="arch" type="xml">
            <field name="name" position="before">
                <field name="company_group_id" />
            </field>
            <filter name="group_company" position="before">
                <filter
                    name="group_company_group"
                    string="Company Group"
                    context="{'group_by': 'company_group_id'}"
                />
            </filter>
        </field>
    </record>
</odoo>

<?xml version="1.0" encoding="UTF-8" ?>
<odoo>
    <record id="view_partner_form" model="ir.ui.view">
        <field name="name">res.partner.form</field>
        <field name="model">res.partner</field>
        <field name="inherit_id" ref="base.view_partner_form" />
        <field name="arch" type="xml">
            <field name="vat" position="before">
                <field
                    name="company_group_id"
                    attrs="{'invisible': [('is_company','=', False)]}"
                />
            </field>
        </field>
    </record>
    <record id="view_res_partner_filter" model="ir.ui.view">
        <field name="name">res.partner.select</field>
        <field name="model">res.partner</field>
        <field name="inherit_id" ref="base.view_res_partner_filter" />
        <field name="arch" type="xml">
            <field name="name" position="after">
                <field name="company_group_id" />
            </field>
            <filter name="group_company" position="before">
                <filter
                    name="group_company_group"
                    string="Company Group"
                    context="{'group_by': 'company_group_id'}"
                />
            </filter>
        </field>
    </record>
</odoo>

Change group search field after name
[IMP] partner_company_group: Change group search field after name
