ANZ has rebranded its online share trading business, changing the name from E*Trade to ANZ Share Investing.The bank said in a media release that it made sense to use the ANZ brand for the business.E*Trade was launched in Australia in 1998 and became a wholly owned subsidiary of ANZ in 2007.In its early years it was an innovator in the execution-only broking market and enjoyed a high profile. Under ANZ's ownership it has made few innovations and has lost its profile.This is evident in Investment Trends market share data, which shows E*Trade losing share over the years.It is also evident in the latest Canstar online share trading ratings. Canstar gave CMC Markets the award for best broker and gave outstanding value ratings to Commonwealth Bank's CommSec, Westpac and nabtrade in different categories.E*Trade didn't rate a mention.