If you want to assign the text to first Item of your Repeater control the please add this block of code in your Button Click event.
string name = "Azim";
(this.rptUsersNames.Items[0].FindControl("lblName") as Label).Text = name;
HTML
<asp:Repeater ID="rptUsersNames" runat="server">
<ItemTemplate>
<asp:Label ID="lblName" Text='<%# Eval("Name") %>' runat="server" />
</ItemTemplate>
<SeparatorTemplate>
<br />
</SeparatorTemplate>
</asp:Repeater>
C#
protected void Page_Load(object sender, EventArgs e)
{
if (!this.IsPostBack)
{
Session["Date"] = DateTime.Now;
DataSet ds = new DataSet();
DataTable dt = new DataTable();
dt.Columns.AddRange(new DataColumn[3] { new DataColumn("Id", typeof(int)),
new DataColumn("Name", typeof(string)),
new DataColumn("Country",typeof(string)) });
dt.Rows.Add(1, "John Hammond", "United States");
dt.Rows.Add(2, "Mudassar Khan", "India");
dt.Rows.Add(3, "Suzanne Mathews", "France");
dt.Rows.Add(4, "Robert Schidner", "Russia");
this.rptUsersNames.DataSource = dt;
this.rptUsersNames.DataBind();
}
}
protected void GetValue(object sender, EventArgs e)
{
string name = "Azim";
(this.rptUsersNames.Items[0].FindControl("lblName") as Label).Text = name;
}