What does the term tryambaka mean? We hold that it means mother -> goddess. This is supported by the fact the ritual devoted to this form of rudra also invokes the goddess ambA. The ritual sUtra-s mention the 3 rudrian goddess rudrANI, bhavAnI & sharvANI – pAraskara of SYV tradition. Thus, the form tryambaka is one with the 3 goddesses. The association of rudra with a group of goddesses is also alluded to in the shatarudrIya and the AV texts. Thus, tryambakA means the one with the 3 goddesses. This triadic structure of the rudrian goddesses continued into the tantras with three bhairavI-s of the trika-kaula stream.
The YV and SV explicitly refer to tryambaka as rudra.