If you want to change the page title from a webpart on the page for example, you could use this:
private void ChangeTitle(string newTitle)
{
SPListItem item = SPContext.Current.ListItem;
if (item != null)
{
item[SPBuiltInFieldId.Title] = newTitle;
item.SystemUpdate(false);
}
}
This will only work for a page in the pages library, because the default.aspx page in the root of your site doesn't have an associated listitem. Also don't forget to refresh your page after changing the title.
The SystemUpdate makes sure that 'modified/modified by' information is not updated and that the version number doesn't increase. If you want this information updated, replace it by item.Update();