Try this:
string strConn = "Data Source=SEZSW08;Initial Catalog=Nidhi;Integrated Security=True";
SqlConnection Con = new SqlConnection(strConn);
Con.Open();
string strCmd = "select companyName from companyinfo where CompanyName='" + cmbCompName.SelectedValue + "';";
SqlCommand Cmd = new SqlCommand(strCmd, Con);
SqlDataAdapter da = new SqlDataAdapter(strCmd, Con);
DataSet ds = new DataSet();
Con.Close();
da.Fill(ds);
cmbCompName.DataSource = ds;
cmbCompName.DisplayMember = "CompanyName";
cmbCompName.ValueMember = "CompanyName";
cmbCompName.Enabled = true;
If it is a drop down then use
ddlCompName.Datasource=ds;
ddlCompName.Datavaluefield="CompanyName";
ddlCompName.DataTextfield="CompanyName";
ddlCompName.DataBind();
[Edit]Code blocks added[/Edit]