"Ten Commandments" is not a mistranslation of עֲשֶׂרֶת הַדְּבָרִים, but is justified based on the Hebrew and Greek Bibles themselves.

The meaning of דָּבָר in the Hebrew Bible

In the Hebrew Bible (the Old Testament), though the word דָּבָר commonly means "a word," it has a wide range of meanings based on its root meaning (on which see the next subheading below). Here are the meanings given for דָּבָר in the Gesenius Hebrew and Chaldee Lexicon:

(1) word, often collective: words, speech, discourse
   (a) a promise, something promised
   (b) a precept, an edict
   (c) a saying, a sentence (as of a wise man), especially the word of the Lord, an oracle
   (d) a counsel, proposed plan
   (e) rumor, report
(2) thing, thing done, affair, business
(3) anything, something
(4) a cause, reason
(5) cause (in a forensic sense)

Clearly the text in Exodus 20:1-17 and Deuteronomy 5:6-21 cannot be described literally as "ten words." There are far more than ten words in these passages. At minimum, דָּבָר in this context means a saying of the Lord. But these are more than "sayings." They are, in fact precepts or edicts, in line with definition (1)(b).

This is the basis on which עֲשֶׂרֶת הַדְּבָרִים is commonly translated into English as "the Ten Commandments" where it appears in Exodus 34:28; Deuteronomy 4:13; 10:4. (עֲשֶׂרֶת is a form of the Hebrew word עֶשֶׂר (`eser), "ten.")

Further, this is not the only context in which דָּבָר is translated as "commandment." As seen in its definition in Gesenius linked above, the King James Version translates it as "commandment" twenty times. The search algorithm used at the linked site to identify those occurrences is flawed, giving many more results than it should. Here are the actual verses in which the KJV translates דָּבָר as "commandment":

1. Exodus 34:28
2. Deuteronomy 4:13
3. Deuteronomy 10:4
4. Joshua 8:8
5. 1 Samuel 15:11
6. 1 Samuel 15:13
7. 2 Samuel 12:9
8. 1 Chronicles 28:21
9. 2 Chronicles 31:5
10. Esther 1:12
11. Esther 1:19
12. Esther 2:8
13. Esther 3:15
14. Esther 4:3
15. Esther 8:14
16. Esther 8:17
17. Esther 9:1
18. Psalm 103:20
19. Daniel 9:23
20. Daniel 9:25

The first three are the familiar "Ten Commandments." The instances in Esther refer to commandments of King Ahasuerus. Most of the rest refer to commandments of the Lord. In each case, though דָּבָר could be translated as "words" or "sayings," its most natural and reasonable meaning in context is that of a "commandment" of the Lord or of a powerful human being such as a king. These are "sayings" that are meant to be obeyed. In other words, they are edicts, or in more common English, commandments.

The root meaning of דָּבָר

The word דָּבָר is a noun form coming from the root דָּבַר, whose core meaning is not "word" but rather "setting in a row, ranging in order." As a verb it is used of leading, guiding, ruling, directing, and of course in its most common meaning of "speaking," or "putting words in order."

This derivation of דָּבָר shows that both in its verb form and as a noun it has more force than the more informal (and also very common) Hebrew word אָמַר, referring to common conversation and speech. דָּבָר has more of a sense of directed, purposeful speech intended to arrange things and bring them into order.

In short, based on its root meaning, דָּבָר lends itself to being used of "words" that are edicts, precepts, and commandments.

Support in the Greek Bible

The term "Ten Commandments" or "Ten Words" does not occur in the Greek Bible (the New Testament).

However, in the Gospels Jesus does refer to various of the "sayings" in the Ten Commandments as "commandments":

Then someone came to him and said, "Teacher, what good deed must I do to have eternal life?"

And he said to him, "Why do you ask me about what is good? There is only one who is good. If you wish to enter into life, keep the commandments."

He said to him, "Which ones?"

And Jesus said, "You shall not murder; You shall not commit adultery; You shall not steal; You shall not bear false witness; Honor your father and mother; also, You shall love your neighbor as yourself." (Matthew 19:16-19, New Revised Standard Version, emphasis added)

Here, when Jesus is asked which commandments are to be followed, he lists five of the Ten Commandments, plus one other commandment from Leviticus 19:18.

See also the parallel passages in Mark 10:17-19 and Luke 18:18-20.

The Greek word for "commandment" used here is ἐντολή, which is a basic Greek word for an order or command.

A similar usage occurs in the Epistles:

Owe no man any thing, but to love one another: for he that loveth another hath fulfilled the law. For this, Thou shalt not commit adultery, Thou shalt not kill, Thou shalt not steal, Thou shalt not bear false witness, Thou shalt not covet; and if there be any other commandment, it is briefly comprehended in this saying, namely, Thou shalt love thy neighbor as thyself. (Romans 13:8-9, KJV, emphasis added)

Many newer translations supply "commandment" where the Greek more literally reads "For this" in verse 9. However, "commandment" (ἐντολή) does appear where I have added emphasis, showing that Paul also referred to the "sayings" of the Ten Commandments as commandments.

These examples from the New Testament show that as early as the first century, the "sayings" of the Ten Commandments were referred to as "commandments."

Conclusion

It is not necessary to look to subsequent Christian history to find the basis for translating עֲשֶׂרֶת הַדְּבָרִים as "the Ten Commandments."

The word דָּבָר itself carries that meaning and force based on its root meaning and on its usage in various contexts in the Hebrew Bible.

Further, the directives comprising the Ten Commandments are referred to as "commandments" in the New Testament, suggesting that in the first century this was already a well-established common understanding of עֲשֶׂרֶת הַדְּבָרִים.

Later English translations of עֲשֶׂרֶת הַדְּבָרִים as "the Ten Commandments" are therefore neither mistranslations nor innovations, but draw on a usage long established in the Hebrew and Greek Bibles themselves.