Well, “Shlomi” or “שלומי” in Hebrew (see its wikipedia entry) means “my Shalom” in Hebrew, or perhaps “Shalom-ful” (= having the property of Shalom) or “the Shalom of Jehovah”. “Shalom” is an ancient Hebrew word, that is derived from proto-Semitic origins meaning something like “well-being”, “welfare”, “peace”, “harmony”, etc. It is an ambiguous noun as the nouns of some ancient Semitic languages were. See also what I wrote about it on my blog (and some of the comments I received).

The reason why it is “Shlomi” or “Shelomi” instead of “Shalomi” is due to a certain pronunciation transformation in Hebrew, where certain vowels are shortened into a Schwa when they are distanced too much from the Stress of the word. Quite a few non-Hebrew speakers have issues with pronouncing Hebrew words that start with several Schwas in succession (as this scene from a screenplay I wrote indicates).

Now, most Israelis pronounce this name with the stress on the “lo”. I, however prefer it to be pronounced with the stress on the “mi”, albeit I also answer to people who pronounce it the other way around. My version is the correct Biblical pronunciation. You can hear me pronounce it in Hebrew (Ogg, mp3) and in English (Ogg, mp3).

Please spell the name as starting with “Sh”, similar to the common spelling in English — not with “Sch” (the German spelling).

My last name - Fish - naturally means the aquatic creatures in English or (with a different spelling) in German. It was the last name of my late grandfather who was a Polish-born Jew, and I’m still carrying it.

“Fish” is an uncommon name in Israel, but there are also some variations such as “Fisher”, “Fishman”, “Fischer”, “Fishlov”, “Fishelson”, etc.

Note that the last name “Fish” is not meaningful in Hebrew and in fact in Ancient Hebrew the only possible pronunciation would be “Pish” (which means “pee” or “urine” in Modern Israeli Hebrew slang) because it uses the same letter - פ for both the "P" and the "F" sounds, and it would be "P" in the beginning of the word.