Sue is pronounced, [su:] and Susan is pronounced various ways,
 the 'u' in under, [su:zən]
 the 'e' in bed, [su:zɛn]
 the 'i' in sit, [su:zIn]
 no vowel [su:zn]
Note, the 2nd "s" is pronounced [z]
Click on the link below to hear the sounds for the vowels [ə], [ɛ], [I], [æ].
Edited to add IPA (International Phonetics Alphabet)