Abbreviating names that start with a vowel

When abbreviating all kinds of names, the first letter is taken:

David Jones / D. Jones
James McKenzie/ J. McKenzie
Esther Hart / E. Hart
Otis Witherspoon/ O. Witherspoon

In normal English usage, abbreviations of names are based only on the first letter as spelled. This is true for first, middle, and last names:

• John Edgar Hoover → J. Edgar Hoover
• Dwight David Eisenhower → Dwight D. Eisenhower
• John Smith → John S. (common for e.g. schoolchildren, if there is another John in the same class)
• John Fitzgerald Kennedy → John F. Kennedy → JFK

and regardless of pronunciation:

• Philip /ˈfĭlĭp/ → P. (whereas Felipe → F.)

Therefore, you would abbreviate your example as

• Alanis Morissette → A. Morissette

There are 2 exceptions I can think of.

• First, nicknames may be formed irregularly; for example "McDonald" → "McD".
• Second: in the most common transliteration scheme from Cyrillic to Latin, some Cyrillic letters get mapped to 2 or more Latin letters. When transliterating abbreviated names from Cyrillic, usually both are kept (only the first is capitalized). Example: Цахиагийн Элбэгдорж → Ц. Элбэгдорж → Ts. Elbegdorj

This only applies to transliterations from foreign languages. So, for example, in text written originally in English, Russian-American Sergei Khrushchev's name would be abbreviated "K.", not "Kh.".

It's uncommon in the U.S. to use anything more than the first initial – consonant or vowel. However, one rare but interesting exception is when two players on the same athletic team share the same last name, and the same first initial. In such circumstances, sometimes the second letter is used to differentiate between, say, Michael and Martellus.