In American English, the only difference between the traditional pronunciation of Salome
and "salami" is the vowel in the stressed middle syllable, which rhymes with "hoe" in Salome
and "hah" in salami.
There are quite a few American women with the name, however, who pronounce it as "sah-lo-MAY". This was originally the French pronunciation of the name, and became current in certain circles because it was the name of a play written by Oscar
Wilde in French which later was the basis of an opera by the German
Strauss. Many people, especially those who were opera buffs, seem to have taken up the pronuciation of the name used in the opera without realizing that it was not the same as the traditional English pronunciation of the name.