The original names of some of the letters of the Latin alphabet are disputed.
In general, ancient Romans did not use the traditional Greek (Semitic-derived) letter names.
The names of the stop consonants (b, j, k, p, t) were formed by adding /ei/ to their sound. The exceptions to this rule were K and Q, since they needed different vowels to be distinguished from letter C.
The names of continuants were either their bare sound, or their sound preceded by /e/.
Letter Y when first introduced, was supposedly called hy /hyi/ as in Greek, since the term upsilon was not in use yet. However, its name was later changed to i Graeca (Greek i) since Latin speakers had difficulties telling apart the foreign sound /y/ from /i/.
Letter Z was given its Greek name, zeta.
To get the best idea of ancient Latin letter names from a modern language, have a look at German alphabet. German language has been most conservative in preserving the ancient Roman letter names.