Why were the interpreters called "Urim and Thummim"? Urim and Thummim are lots in the pouch of the priests (High Priest? I don't remember) in the Old Testament. Not sure what &quot;lot&quot; is in this context but I am imagining some kind of dice. In any case, sometimes the lot were cast and the result seen as manifestation of divine will. Revelation.
The interpreters (on the breastplate which Joseph Smith got together with the plates) were clear stones you would look into and see something. Joseph Smith used them to translate the Book of Mormon, and I suppose there could be some other revelations he had through them.
The connection is both are physical objects used to inquire God and receive revelation, but that's about it. It's not even obvious whether or not the Urim and Thummim were stones (right?). The interpreters are more like the Liahona than the Urim and Thummim in my mind. The Book of Mormon, as far as I am aware, doesn't use the term &quot;Urim and Thummim&quot;, nor does any angel that visited Joseph Smith (right?). The interpreters appear in the Book of Mormon from nowhere, as far as I am aware, King Mosiah just happens to have them.
So why did (I assume Joseph Smith) start calling them &quot;Urim and Thummim&quot;? Just to give them a biblical name or is there something more to it? And when did this association start?
Well, a simple search would have revealed that the association is (contrary to the question claiming otherwise) made in D&amp;C 10:1:

1 Now, behold, I say unto you, that because you delivered up those
writings which you had power given unto you to translate by the means
of the Urim and Thummim, into the hands of a wicked man, you have lost
them.

And even earlier, Moroni himself in Joseph Smith - History 1:35:

35 Also, that there were two stones in silver bows - and these stones
fastened to a breastplate, constituted what is called the Urim and
Thummim [...]

I also found this question on BH.SE which has the following insights which are somewhat consistent with Joseph's Urim and Thummim:

the OT's Urim and Thummim were on or in a breastplate
they could give complex answers, and in one case also no answer
some views say they were actually the twelve stones and illuminated to give answers, some more exotic views even speaking of letters moving on the stones

But all in all, it's not clear what they were, the Bible doesn't tell much about them, just that they were in some relation to the breast plate of the high priest and were used to inquire God.