Similarities in names are a judgement call. You believed that the names were sufficiently different, google's lawyers did not - and to be honest as soon as I read neuoogle I related that to google, so IMO they are sufficiently similar for an individual with no previous experience with your app to associate the two. Also, as you were going for trade mark of your name, you would (or should) be aware that trade marks can be lost if not defended. The google lawyers are just defending the google trade mark against attempts to trade mark words (or whatever) that are sufficiently similar to theirs that a regular person may believe that your app is being represented by google (or whatever).
The fact that you chose a name that differed from google in only the prefixed letters, you almost invited the lawyers to your door. I will assume that you chose the name as you wanted your app associated with the google term which could be considered synonymous with "searching the internet". If the google lawyers didn't protect google's trade mark, it would soon fall into the realm of kleenex, or cling wrap; Once trade marked names that were not defended.
Perhaps in the future you would find a name that is far enough removed from the trade mark of giant companies to ensure the giant companies don't start exercising their legal right in protecting their trade marks.
I am based in Sydney and have done some graphic work, feel free to send me your assets plus your new name (if you think of one) and I'll update the assets for you free of charge. (p3r AT users.sourceforge.removeme,net)