When I posted the snippet to allow you to restyle of My Notes, I hadn't thought that it wasn't as straight forward to change the title of Phrase of the Day. This bit of CSS is the easiest way I've found of changing all Phrases of the Day, although if you combine it with the the technique(?) mentioned in the restyling My Notes, you can restyle individual widgets in the same way.
<style>
.widget_phrase-wrap .header {
height:50px;
overflow:hidden;
}
.widget_phrase-wrap .header h2::before {
content: 'My own title \a';
white-space: pre;
}
</style>