One would think that changing some text of a tab would be pretty trivial, especially since the ajax TabContainer control contains this function...

set_headerText : function(value) {
        if (!this.get_isInitialized()) {
            throw Error.invalidOperation(String.format(AjaxControlToolkit.Resources.Tabs_PropertySetBeforeInitialization, 'headerText'));
        }
        if (this._headerText != value) {
            this._headerTab.innerHTML = value;
            this.raisePropertyChanged("headerText");
        }
    }

This function didn't work as simply as I had imagined

Through my testing I was getting various javascript errors as I tried random things. The most frustrating error I was receiving was

'Microsoft JScript runtime error: 'this._headerTab' is null or not an object'Why is this null or not an object. It shows up in the browser correctly and get_headerText returns the correct value!?

Bypassing this function call was the only other option. This was achieved by the following javascript code

$find('<%= TabContainer.ClientID %>').get_tabs()[0]._header.innerHTML = 'Changed';

 Maybe the ajax tab.js file has an error and is setting the wrong property and instead of

this._headerTab.innerHTML = value;

it should be

this._header.innerHTML = value;

Below is the asp markup for the test and http://forums.asp.net/ a decent forum thread on a similiar topic.

<ajaxToolkit:TabContainer ID="TabContainer" runat="server" ActiveTabIndex="0" CssClass="ajax__tab_xp"
                        EnableViewState="false">
       <ajaxToolkit:TabPanel ID="Tab1" runat="server" HeaderText="Change ME">
               <ContentTemplate>text
               </ContentTemplate>
       </ajaxToolkit:TabPanel>
</ajaxToolkit:TabContainer>