As we all who know Hebrew can assert, the sufix "im" in the words usually means plurality. How can HaShem be Elohim or Elokim if He is absolutely One and the Only Lord?
There are a lot of answers. Here are a couple:
In Hebrew, mastership is often expressed in the plural, as in אדוני יוסף or בעליו עמו. Similarly, then, the Name Elokim, which denotes that G-d is Master of the Universe, is in plural form (and sometimes even takes plural-form verbs). (Rashi to Gen. 20:13 and 35:7)
It's the plural of אלה, "these." This Name represents G-d as the master and controller of all of the disparate "these-es" of creation. (R' S.R. Hirsch to Gen. 1:1)
In a similar vein, though in Kabbalistic terms: Elokim is in plural form because it symbolizes the different spiritual worlds and levels which G-d created to serve as the conduits for His energy to reach the physical world and power it. (R' Shneur Zalman of Liadi, Torah Ohr, Vayera 56a ff)
There are an abundance of answers given to this question, including those listed by Alex.
You might like the approach of Abarbanel, who sees no reason to assume that "elokim" is plural, since it is used as a name, like Ephraim, Mitzraim, or Chushim, which are all names in the "plural form". Rather he prefers the explanation that "elokim" is a composition of "el" meaning "god" in a general sense, and God's specific four-letter name ykv"k. (The me"m at the end of the name is to be grammatically correct in "closing off the word" so it won't sound like a possessive noun.)
כל לשון יש לו דרך כבוד. וכבוד ל' לועז שיאמר הקטן לנוכח הגדול לשון רבים. ובל' ישמעאל דרך כבוד שידבר הגדול כמו המלך בלשון רבים ובל' הקדש דרך כבוד לומר על הגדול ל' רבים כמו אדנים בעלים שאמרו אדנים קשה. ולקח בעליו.
Every language has an honorific mode. . . in Lashon Hakodesh the honorific mode is [expressed by] speaking about a superior in plural terms. . .
I like the analog to the English "royal we".
R. Judah Halevi addresses this question right in the beginning of Part IV of the Kuzari:
The word has a plural form, because it was so used by gentile idolaters, who believed that every deity was invested with astral and other powers. Each of these was called Eloah; their united forces were therefore, called Elohim.
(Hirschfeld translation p. 198)
Apparently, then, the Torah uses the word Elohim because it conveys the idea of the sum of all powers, which is what God is, and not to impugn the unity of God.
A name represents the function of the entity who holds it—i.e., how they interact with the world. Jewish names are supposed to reflect the purpose of the child, which is the reason for how they interact with the world, and therefore, parents are given a certain amount of prophecy to name their child the correct Hebrew name.
G-D doesn’t have a purpose. G-D is the One who needs the purposes for His plan. Therefore, His Names each represent one of the ways in which He interacts with the world. His Name “Eloqim” translates to “Powers”, and means He interacts with the world via every single one of the powers in creation, which are all under His control. It is His Name of Judgement, of Awe, of Control, of Creation. His Name “Adoqai” translates to “My Masters”, and means that He is the King of Kings of Kings, the Ruler of all the forces of creation, and the One Who directly causes the causes and results of anything and everything to occur. It is His Name of total Mastery. So on with all His Names. The two I used as examples are in the multiple, answering your question more directly.
kabbalistic literature differentiates between G-ds intrinsic name (the Tetragrammaton) which refers to his essence of absolute unity, and than other names which refer to various attributes of G-d. Elokim refers to the fact that G-d is the master of all forces in the world. The name specifically comes to address the fact that in the universe there appears to be disparate forces and that G-d is the master of all of them. Elokim is a name that specifically addresses how G-d appears from our perspective where there is not absolute unity. Much of Sefer Nefesh Hachaim comes to address this. See the first few chapters that explain the name Elokim.