Uso de xml.modify para insertar parámetros en un elemento específico de una columna xml

declare @XML xml = '
<Profile>
  <ID>20</ID>
  <User>
    <ID>BC4A18CA-AFB5-4268-BDA9-C990DAFE7783</ID>
    <Name>somename</Name>
    <Activities>
      <Activity>
         <Name>activity1</Name>
      </Activity>
    </Activities>
  </User>
</Profile>'

declare @user_id nvarchar(50) = '20'
declare @activity_name nvarchar(50) = 'activity1'
declare @display_name nvarchar(50) = 'displayname1'

set @xml.modify('insert <DisplayName>{sql:variable("@display_name")}</DisplayName>
                 into (/Profile[ID = sql:variable("@user_id")]
                       /User/Activities/
                       Activity[Name = sql:variable("@activity_name")])[1]')

Resultado:

<Profile>
  <ID>20</ID>
  <User>
    <ID>BC4A18CA-AFB5-4268-BDA9-C990DAFE7783</ID>
    <Name>somename</Name>
    <Activities>
      <Activity>
        <Name>activity1</Name>
        <DisplayName>displayname1</DisplayName>
      </Activity>
    </Activities>
  </User>
</Profile>