You could do it like:

<?xml version="1.0" encoding="UTF-8"?>
<templates xml:space="preserve">

   <t t-extend="mail.ChatThread.Message">
      <t t-jquery=".o_mail_timestamp" t-operation="replace">
         <small class="o_mail_timestamp" t-att-title="message.date">
            <t t-esc="message.date"/>
         </small>
      </t>
   </t>

</templates>

Using different values for t-extend and t-name will create a new template with the value name of t-name that will inherit from the template with the value name of t-extend. Like models prototypal inheritance

Using just t-extend will inherit the original template in-place without creating a new one. The same applies for using only t-name overriding completely the original template and also using t-extend and t-name with the same value of the original template creating a new template with the name of the original one that inherits from that original one (no need to complicate it like that but works)