How to edit SharePoint page using client Object Model

Here is a console application that does what you want. Below i am getting the file by server relative URL, you could either get them directly by iterating the collection of items from the list.

string pass = "<your-password>";
SecureString ss = new SecureString();
foreach (char c in pass)
{
    ss.AppendChar(c);
}
using (ClientContext ClientWebContext = new ClientContext("<site-collection-url"))
{
    ClientWebContext.Credentials = new SharePointOnlineCredentials("<your-username>", ss);
    List li = ClientWebContext.Web.Lists.GetByTitle("Pages");
    Microsoft.SharePoint.Client.File f = ClientWebContext.Web.GetFileByServerRelativeUrl("<relative-path-of-your-file>");
    ListItem item = f.ListItemAllFields;
    ClientWebContext.Load(item, i => i["FileLeafRef"]);
    item.File.CheckOut();
    ClientWebContext.ExecuteQuery();
    item["FileLeafRef"] = "Newname.aspx";//some new file name
    item.Update();
    ClientWebContext.Load(item);
    ClientWebContext.ExecuteQuery();
    item.File.CheckIn("Check-in",CheckinType.MajorCheckIn);
    ClientWebContext.ExecuteQuery();
}