Complex sentence: Google's intention, as expressed in the developer documentation, was that Chromium would be the name of the open source project and that the final product name would be Chrome, however other developers have taken the Chromium code and released versions under the Chromium name.
Split into simpler sentences: Google's intention, as expressed in the developer documentation, was that Chromium would be the name of the open source project and that the final product name would be Chrome. However, other developers have taken the Chromium code and released versions under the Chromium name.