Trouble theming poll block in Drupal 6
If all you are just trying to change is the layout of the form, and not the data contained in it, all you should need to do is change the CSS for the various wrappers.

In this example, that would be looking at

&lt;div class="poll"&gt;
  &lt;div class="vote-form"&gt;
    &lt;div class="choices"&gt;
      &lt;?php if ($block): ?&gt;
        &lt;div class="title"&gt;&lt;?php print $title; ?&gt;:&lt;/div&gt;
      &lt;?php endif; ?&gt;
      &lt;?php print $choice; ?&gt;
    &lt;/div&gt;
    &lt;?php print $vote; ?&gt;
  &lt;/div&gt;
  &lt;?php // This is the 'rest' of the form, in case items have been added. ?&gt;
  &lt;?php print $rest ?&gt;
&lt;/div&gt;


so, if in your theme CSS you added

.poll {
  color: red;
  background-color: blue;
}


this block would now be in red and blue.

and if you added

.vote-form {
  border: 2px solid green;
}


then the form would have a border of green.  etc etc etc.

Now, if you need to change things up more, add some more divs or change their order, etc, you can just copy the standard poll template to your theme directory, refresh your caches and drupal will pick it up and override the one from poll itself, no need to name it anything different.