Regarding the type of question "why this and not that?":
Sanhedrin 91b
Guide for the Perplexed 3:26 (Rambam)
Wars of the Lord Introduction (Ralbag)
Hence the reader should not inquire concerning these things why we have treated this thing before some other thing, since [he thinks] that the other thing should be treated first because of one of the aforementioned reasons. weWe have in fact treated one particular subject first precisely because of one of these reasons: and it is obvious that if we had adopted the reverse order the same question would have been raised. (Feldman translation)
Regarding specifically the usage of different names of God:
Emunos V'deios 2:3 (Sa'adia Gaon)
ואם יאמר אדם מה ענין שני שמות הללו המשומשים תמיד במקרא ה' אלהים נאמר כבר קבע שהם לענין אחד כאמרו כי כה אמר ה' בורא השמים הוא האלהים ואמרו דעו כי ה' הוא האלהים הוא עשנו וגו' ואחר הקביעה הזו אין לחוש אם יתאר אחד מהם בפעולה אחרת ודומה לזה בלשון וילך ירובעל בן יואש וישב בביתו ואמר אחריו ולגדעון היו שבעים בנים יוצאי ירכו תיאר שם זה בפעולה והשני בפעולה אחרת ולא חש כיון שכבר קבע בדבריו כי ירובעל הוא גדעון (Kafih translation p. 87)
Now if someone were to ask: "But in that case what is the meaning of these two names 'Ădhonay and 'Ĕlohim that are constantly employed in the Bible with reference to God?" our answer would be that Scripture makes it quite clear that they both have one connotation. This is borne out by its statement: For thus saith the Lord that created the heavens, He is God (Isa. 45:18), as well as its statement: Know ye that the Lord He is God (Ps. 100:3).
After this definition, then, no attention is to be paid to the fact that one of these two appellatives is used in the description of one action whilst the other is used in describing another, for there is many a parallel to this usage in the language of Scripture. Thus it states: And Jerubbaal the son of Joash went and dwelt in his own house (Judg. 8:29), and after that: And Gideon had three-score and ten sons of his body begotten (Judg. 8:30). One name is here used in the description of one act and another in connection with another without any scruple, because it has already been definitely stated that Jerubbaal was identical with Gideon. (Rosenblatt translation p. 99)
The implication is that once we know God's names it makes no difference which name is used in which context. Indeed, Rosenblatt in his footnote to the above passage writes:
Saadia undoubtedly has in mind such statements as the one quoted in Genesis Rabba (xxxiii) on genesis 8:1 to the effect that the name 'Ădhonay stands for God's quality of mercy, whereas that of 'Ĕlohim betokens His quality of justice.