Answer:
   
   Here is an explanation of some of the names used:
     * E-lohim (el-hiym). "Lawmaker", both in the sense of nature and in
       that of moral and religious law. In Exodus, the legislators of the
       human court are refered to as elohim. The plural is perhaps a
       statement of majesty, or perhaps the idea that G-d is the Author
       of all laws. Not that the two are all that different. The majestic
       plural comes from the idea that the king or queen spoke for all of
       England. Jewish tradition notes that this name is used in
       naaratives where G-d's actions can more readily be seen as pure
       justice.
     * El. Almighty. Same root as E-lohim.
     * Y-H-V-H. Literally "the self existent" implying "eternal".
       Sometimes this is rendered as "I am", but this doesn't really
       express the significance behind what is implied with this word.
       This word is harder to translate because the vowels have been
       lost. The usual "Ye-hovah" is actually the vowelization of
       "A-donai" (my L-rd[s]), adapted for the consonants. The leading
       yud can't take the almost-schwa short /a/ sound, so it is written
       with a schwa instead. The word can also be taken to mean "the
       Causer of existance". Also, midrashically, the tetragrammaton is
       taken as a contraction of "hayah, hoveh, yihyeh -- was, is, will
       be".
     * Ad-nai. Supreme Lord or sovereign. Again, literally it means "my
       L-rd[s]".
       
   Does the grammar or use a unique one or singular being, as compared to
   that implied by the use of the plural? Not really, because the
   adjectives and verbs used with these names are consistantly singular.
   The name can't be intended as a plural, which is a second reason,
   aside from the monotheistic theology.
   
   There is more information in answer [5]9.11.