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It makes your url a lot easier to remember and will lead to returm visits. I also belive that having your own domain will help you out getting good placement on search engines.
As for adsence, So long as you ensure that the domain is registered in your name (not your hosts) then you should be in with a good chance of being acepted.
I have a question, which may seem silly, but may also be relevant. Because a lot of the stuff on my site is related to online games, I use my gaming nick to identify myself, if you know what I mean, Hi I'm B...a, welcome blah blah... Should I remove this sort of thing and use my real name? And should I go even further, and remove the personal greeting, and just have a typical news section pointing to the latest additions? I'm just wondering how 'personal' is personal?
Oh... how personal is personal? That depends as well but there are some definitive things I go by. A "personal" site in my opinion is one that's content is solely about the person developing the site. But there is also another side of that coin in that some people create "personal" web sites but have gobs of other useful, non-personal content (from the sounds of things, what you've done). These kinds of sites are what make the web what it is today.
My general rule of thumb is to keep away from real names.
Depends on the type of site you have, I guess. If I were publishing a bondage site or a community-oriented site for the kind of people who buy "This vehicle insured by Smith & Wesson" bumper stickers, I might use a pseudonym. But for many topics, a real name offer credibility while building a long-term brand identity.
In my field--European travel--there's a long tradition of using real names. Karl Baedeker, Eugene Fodor, Temple Fielding, Arthur Frommer, Karen Brown, and Rick Steves are just a few of the writers and writer/publishers who have developed brand identities and the trust of their readers by placing their bylines on the covers of their guidebooks. I do the same thing with my editorial Web site, and it's one of the things that differentiates my site (and the sites of guidebook authors like Rick Steves and Karen Brown, for that matter) from corporate sites like Lonely Planet, Rough Guides, or Time Out.
Are you sure you gave it long enough for the DNS of you new registration to be picked up across the web. It could be that they looked at you "old" url, as the "new" one was not showing. As far as I can see you registered and applied to Google in under 24 hours of registration.
It is worth putting old and new on email and asking for clarification that they did reject your "new" url