Sage Ramakrishna has said: I have seen many forms of Gods and Goddesses; but I have never seen one more charming than tripurasundarI!
The word soundaryam pertains to SundarI and means The Beauty.
But the beauty of it all is, that the name tripura-sundarI or any of the other (synonymous) names of the same form, namely, LalitA, RAjarAjeshvarI, KAmAkshI or KaAmeshvarI do not occur anywhere in the text, including its title !
Even the other descriptive names of the Goddess like hima-giri-sutA (daughter of Himalaya mountain), or simply, giri-sutA, shivA, bhavAnI, umA, satI, pArvatI, chanDI occur only at one or two places.
General attributed names, like jananI, mAtA, ambA, devI meaning either mother or goddess, -- which commonly go with all feminine deities -- occur at a few more places, but even they are few.