What the lexicon says. כִּלְיָה (kilyah) is glossed "kidney". Its senses are "of physical organ (lit.)", "of seat of emotion and affection (fig.)" and "of sacrificial animals". Strong's: "A kidney (as an essential organ); figuratively, the mind (as the interior self)." The older English word for it is reins.
Three versions, one word, three organs. At Jeremiah 17:10 the older English keeps the kidneys: "I the LORD search the heart, [I] try the reins" (Jeremiah 17:10, KJV). The ASV prints "I, Jehovah, search the mind, I try the heart" (Jeremiah 17:10, ASV), and the BSB "I, the LORD, search the heart; I examine the mind" (Jeremiah 17:10, BSB). The tagged text has H3629 behind the organ in each case, the differences are entirely in English.
It happens twice more in the Psalms. At Psalm 16:7 the KJV has "my reins also instruct me in the night seasons" (Psalm 16:7, KJV); the ASV has "my heart instructeth me in the night seasons" (Psalm 16:7, ASV); the BSB has "even at night my conscience instructs me" (Psalm 16:7, BSB). At Psalm 139:13 the KJV has "thou hast possessed my reins" (Psalm 139:13, KJV); the ASV has "thou didst form my inward parts" (Psalm 139:13, ASV); the BSB has "For You formed my inmost being" (Psalm 139:13, BSB). Kidneys, heart, conscience, inward parts and inmost being are five English words for one Hebrew noun.
The count. H3629 is in 26 verses and is not split into senses.
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Why this matters for reading, stated narrowly. A reader comparing two English Bibles at Psalm 16:7 sees "heart" in one and "conscience" in the other and may conclude the versions disagree about something. They do not. They are choosing different English words for one Hebrew word that names an organ neither of them prints.
Sources: Jeremiah 17:10 (KJV, ASV, BSB); Psalm 16:7 (KJV, ASV, BSB); Psalm 139:13 (KJV, ASV, BSB); TBESH entry H3629; Strong's Hebrew Dictionary (1890), entry H3629.
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