In addition to Dottard's excellent response regarding the Greek articles, I would point out a few related details from the original Hebrew.
In Hebrew, the article has a grammatical function which converts an otherwise common noun into a proper noun. This is unlike English. In English, if I say "the tree is tall," "tree" is still a common noun. But every Hebrew word prefixed by a definite article is grammatically proper, and made so by the article.
Names in Hebrew do not have articles before them (unlike Greek) because names are already proper.
There are three things that will make a Hebrew word proper (or, more precisely, definite).
- It is a name.
- It has a definite article.
- It has a pronominal suffix.
Any one of these three, or any combination of them, will cause a Hebrew word to become proper. In Hebrew, this has more than just an impact on how "titled" the noun may be. In fact, it has nothing to do with respect at all. It is purely grammatical.
For example, in Hebrew, "the light day" would combine a proper noun "the light" with a common noun "day", thus forming a sentence due to the inequality of the two nouns' "definiteness." The translation would be "the light is day." But if the two juxtaposed nouns are either both common or both proper, and have the same definiteness, they form a Hebrew "construct chain," which means they have a prepositional (e.g. belonging) relationship. So "light day" would be translated as "the light of day."
In the Old Testament, Satan is prefixed by "the" because the word is not a name, and it is made proper, and more specific to "THE" adversary, by the addition of the article. The word "Adam" may help illustrate this, because, without the article, it would generally be translated as "man", yet with the article, which makes it proper, it becomes "Adam." So when we say "the adversary" in Hebrew, the article is what causes it to become a name, i.e. "Satan." (Keep in mind that an article may also be necessary to distinguish between a construct chain and an implied statement of being necessitating the use of "to be" in the translation. However, "Satan" seems not to appear in these forms in the Old Testament.)
Greek articles serve a different function than do Hebrew articles. In Greek, many texts will use the article before Satan, but not all of them do. Greek articles are far more complex than in English, and a definite article in Greek is sometimes properly translated as "the" or as "a/an" or not even translated at all into English.
Essentially, unless one understands Greek grammar well, it would be advisable to be cautious about making unwarranted conclusions from its existence in a particular text. It is not equivalent to English.