Its fairly easy to accomplish this in Ant
use tstamp task.
This is how a set a property "START_TIME" and use it to create that file/folder.
<tstamp>
<format property="START_TIME" pattern="dd_MMM_yy_HH_mm_ss"/>
</tstamp>
Like
<property name="testresults-folder" value="${START_TIME}_TestResults"/>
and create a folder by this property
<mkdir dir="${testresults-folder}"/>