ON A FIRST-NAME BASIS
The Puzzlemaster Presents Vol. 2
Will Shortz (modified)

This puzzle has two parts. Part 2 is much harder than Part 1.

1. Think of a boy's name in one syllable that sounds like a letter of the alphabet. Change this to the next letter of the alphabet to get a one-syllable girl's name that also sounds like a letter of the alphabet.

2. The first syllable of the animal name BEAGLE sounds like a letter of the alphabet - B. Change this phonetically to the next letter of the alphabet and you get - phonetically - the name of another animal, SEAGULL (CEEGLE).

Now, think of a boy's name in two syllables, in which the first syllable sounds like a letter of the alphabet. Change this phonetically to the next letter of the alphabet to get a girl's name of two syllables, in which the first syllable also sounds like a letter of the alphabet.

[In both names, the second syllable also sounds like a letter of the alphabet - the same letter - though  spelled differently.]*

HINTS for Part 2:
A. The boy's name begins with a letter than can have both a hard and soft sound.
B. In this case, it is the hard sound.
C. The girl's name is a bit old-fashioned.

Answers:

Part 1: JAY - KAY

Part 2: CASEY - ELSIE   
             (KC - LC)*

*Added by JA