To all the Kavitas in the world, don't listen to these immature comments. Your name is a poem -- in the literal sense of the word and figuratively. You could write a whole universe with a name like that. Reminds me of a Hopi name I once found... it means 'writer of blossoms'.
I really like this name! It has a great sound and doesn't remind me personally of cavities or caviar. I think people can make too much of certain sounds, and this name in general has a nice sound. Plus, it's spelled with a K whereas cavity and caviar are spelled with C. It also has an awesome meaning- poem! If the cavity resemblance is too much, you can always try the Southern Indian form Kavitha.