tame (adj.) Look up tame at Dictionary.com
early Middle English tame "in a state of subjection, physically subdued, restrained in behavior" (c.1200); of animals "domesticated, reclaimed from wildness," also, of persons, "meek, gentle-natured, compliant, intent on homely or domestic activities" (mid-13c.), from oblique forms of Old English tom, tam "domesticated, docile," from Proto-Germanic *tamaz (cognates: Old Norse tamr, Old Saxon, Old Frisian, Middle Low German, Middle Dutch tam, Old High German zam, German zahm "tame," Gothic tamjan "to tame"), from PIE *deme- "to constrain, to force, to break (horses)" (cognates: Sanskrit damayati "tames;" Persian dam "a tame animal;" Greek daman "to tame, subdue," dmetos "tame;" Latin domare "to tame, subdue;" Old Irish damnaim "I tie up, fasten, I tame, subdue").

A possible ulterior connection is with PIE *dem- "house, household" (see domestic (adj.)). Meaning "spiritless, weak, dull, uninspiring, insipid" is recorded from c.1600. Related: Tamely; tameness.
tame (v.) Look up tame at Dictionary.com
mid-14c., from tame (adj.), or altered by the form of the adjective from Old English temian "subdue, make tame," from Proto-Germanic *tamjan- (cognates: Old Norse temja, Old Frisian tema, Middle Dutch temmen, Old High German zemmen, German zähmen, Gothic tamjan). Related: Tamed; taming.