Is stock history and a company name public domain if the company is publicly traded.?

I have an investment advice website, I have asked public companies for the right to paraphrase company info from their respective sites so I can do analysis and recommendation of the company on my site, including stock price history. I have been ignored thus far after sending repeated emails

Stock price history is information of public record (not "public domain"), the same as baseball scores or the weather. If AT&T traded at a certain price on a certain date, that's a fact, and you can use that fact as you see fit in your analysis.

Paraphrasing company info from their Web sites is a different matter; most Web sites are copyrighted as to their content, so if you choose to include company info other than information of public record, you need to rewrite it so that it's not a direct, word-for-word copy of their site.

You might also, under Fair Use law, be able to include a short description -- a sentence from their mission statement, for example -- as an attributed quotation.

Are you looking for financial info and press releases, etc? If so, any traded company has their info posted on the Yahoo! financial site. Profile, SEC filings, analyst recommendations, etc
See below for an example