The names of most consonants in English contain a common sound of the consonant, plus enough of a vowel sound that the name is a syllable.  In some consonant names, the vowel sound precedes the consonant sound.  In other consonant names, the vowel sound follows the consonant sound.

Consonant sounds at the start of the consonant name:  
`.   B C D     G     J K         P Q     T   V         Z`  

Consonant sounds at the end of the consonant name:  
`.           F           L M N       R S         X`

Vowels:  
`. A       E       I           O           U`  

There are only three exceptions:  
`.               H                             W    Y`  

 * H:  Spanish names its "j" as "ha", so it would be possible to pronounce "H" using its consonant sound + a vowel sound. According to http://wikipedia.unicefuganda.org/latest/A/H.html, the name has mutated over time.  In Latin, "k" and "h" used to have similar sounds.  The name of "H" picked up the "k" sound.  The "k" sound in the name of "H" then mutated to be a "ch" sound in Old French.
 * W:  This letter is named for how it is written -- as a doubled "U" or "V".
 * Y:  This letter is also named for how it is written -- as a combination of "V" and "I".  According to http://wikipedia.unicefuganda.org/latest/A/Y.html, the Romans borrowed the letter "Upsilon" from Greek twice -- once as the letter "v", and once as a "Greek i".