You could add a <br/> to force a line break and define some CSS classes for the font-styling:
<style>
.name { font-weight: bold; }
.subtext { font-size: smaller; }
</style>
<td bgcolor="White" >
<span class="name">First Name</span>  <br/>
<span class="subtext">(on external website)</span>
</td>
Update:
For completeness, I'm also including what others have suggested: instead of using a <br/> element, control the line-break via CSS. This has the advantage, that you can change the behavior (remove the line-break) by simply editing the CSS:
<style>
.name { font-weight: bold; display:block; }
.subtext { font-size: smaller; }
</style>
<td bgcolor="White" >
<span class="name">First Name</span>
<span class="subtext">(on external website)</span>
</td>
Instead of using span elements, you could also use divs, which have the line-break by default (but it can be disabled by setting display:inline in the CSS).