I understand what your trying to do but I don`t think it will work unless you have a strong idea of the perfect market that would choose this over the obvious competition. Renting a domain for $8/day is pricey considering I could buy a possibly better name for just $2/more for the entire year. The only way I can see this working is by targeting the ill-informed mothers and by giving them a very easy interface to customize the greeting message. I recommend you reevaluate your business options and where you see this going. Yes crazy ideas can go wild (eg. million dollar homepage) but a large majority never go anywhere.
As far as the site design, as this is a site critique forum, I like the presentation but I would make the logo go to the all names list or brief description page. Also make the all names link right under the logo or bigger in general. It would probably increase conversions if there was a brief 2-3 sentence description at the bottom. You could still keep the flashing names, but people like Craig may not know what its about or what to do without some more information.
Lastly, I noticed one of the pages had a picture, but it was HUGE and not formatted right. Make it easy for buyers to upload a picture and resize it appropriately, and never larger than a 1024x768 viewspace.
Small Business Website Management and Marketing