I have not been able to find the source of any of the Indian meanings given above. Its phonotactics is right, but I can't find an etymology in Sanskrit. I have not heard the word, and have not met a person with than name, and my best guess is that it is a name patterned after other common names (e.g., tanvi) or that it is a name with a meaning in some regional language (e.g., Hindi/Marathi/etc.; since I know Hindi, I can say it is not a common Hindi word).
Just to be clear, my previous post which gave the meanings "to join" etc., was talking about the verbal root from which nouns could be derived and verbs could be declined; anvi is not a noun with that meaning in Sanskrit.