Is there a name for the decorative, often scrolled, capital letter of the first word of a book or chapter? See the scrolled "T" icon by my user name for an example.
It's called a Drop Cap
The first letter of a paragraph that is enlarged to "drop" down two or more lines, as in the next paragraph. Drop caps are often seen at the beginning of novels, where the top of the first letter of the first word lines up with the top of the first sentence and drops down to the four or fifth sentence.
Drop caps can be anything from highly decorative to merely larger than the following text size.
Smashing Magazine: Drop Caps: Historical Use And Current Best Practices With CSS
MagazineDesign.com: Drop Caps and Initial Letters
The word that you are looking for is illuminated - search for illuminated letters or illuminated characters and you'll find lots of examples.
To clarify and tie in with the other answer, a drop cap (or dropped cap or dropped capital) refers to the practice of enlarging the first letter so that it spans two or more lines of the paragraph that it starts. A drop cap can be in the same typeface as the rest of the text so it's a separate thing to the illuminated characters that you're referring to in your question.