The 1934 book Dictionary of Given Names with Origins and Meanings by Flora Haines Loughead says this about the name's meaning:"A Latin name, meaning: Ara being an altar, and minta relating to the coinage of money, a free translation is sacred coinage."
'This name first appears in American records in the mid-1700s. It is probably an elaboration of the classical Greek name Amynta ("defender"), which was introduced during the Classical Revival period by works such as Edmund Spenser's "Colin Clouts comes home againe" (1595), Henry Purcell's song "Amintas to my grief I see" (1679), and John Dryden's poem "Go tell Amynta, gentle swain" (1680s). These English writers may have borrowed the name from the Italian pastoral play "Aminta" by Torquato Tasso (1573). Note that the original Greek name is masculine; Dryden seems to have been the first to use it as female name. Variations: Arminta, Aramitha, Armitha, Minta, Mintha, Minthy, Minty."