Hi

Is it possible to change language (days,month etc.) ONLY for calendar extender control, without changing culture for complete page?

No, but what you can do is place the textbox in an updatepanel, set AutoPostBack="true" for the textbox, and in the server-side TextBox_TextChanged event, format it however you'd like. 

    Protected Sub TextBox1_TextChanged(ByVal sender As Object, ByVal e As System.EventArgs) Handles TextBox1.TextChanged
        Dim TextDate As Date = CDate(TextBox1.Text)
        TextBox1.Text = TextDate.ToString("MMM dd, yyyy")
    End Sub

Thank you, but maybe I ask different: I want the popup calendar showing up in different languages.

Oh, then no.  The calendar is strictly based on the globalization settings for your application.