Its tricky ;)

<field name="my_field" string="LABEL1" attrs="{'invisible': [('partner_id', '!=', False)]}"/>
<field name="my_field" string="LABEL2" attrs="{'invisible': [('partner_id', '=', False)]}"/>

So, here when you have partner, odoo will display LABEL1 as string.

Other wise LABEL2 for "my_field" field.

You can get some help from here.

Update answer for above answers:

If you looking for solution to inherit view to change the label, try this:

\<\?xml\ version=\"1\.0\"\?\>
\<odoo\>
 \<!\-\-\ show\ custom\ field\ in\ form\ view\ \-\-\>
 \<!\-\-\ inherit\ view\ \"view_partner_form\"\ \-\-\>
 \<record id=\"view_partner_form_inherit\" model=\"ir\.ui\.view\"\ style="color:\#e8bf6a;">\>
 \<!\-\-\ name\ is\ whatever\ you\ like\ \-\-\>
 \<field name=\"name\"\>view.partner.inherit style="color:#e8bf6a;"></field>
 <!-- this model field is the original model -->
 <field name="model">res.partner</field>
 <!-- this inherit_id value is get by "external id" from debug mode view form -->
 <field name="inherit_id" ref="base.view_partner_form"/>
 <field name="arch" type="xml">
 <xpath expr="//page[@name='sales_purchases']//field[@name='user_id']" position="attributes">
 <!-- remove default label -->
 <attribute name="nolabel">1</attribute>
 </xpath>
 <xpath expr="//page[@name='sales_purchases']//field[@name='user_id']" position="before">
 <div>
 <!-- add new label based on condition -->
 <label string="Label 1" attrs="{'invisible':[('partner_id', '=', False)]}" for="user_id"/>
 <label string="Label 2" attrs="{'invisible':[('partner_id', '!=', False)]}" for="user_id"/>
 </div>
 </xpath>
 </field>
 </record>
</odoo>

Hope it helped.