Take datakey as name and take gridview deleting command in gridview and change text name of delete command as per you.
protected void EmployeeGridView_RowDeleting(object sender, GridViewDeleteEventArgs e)
{
string Name= EmployeeGridView.DataKeys[e.RowIndex].Value.ToString();
Response.Redirect("AddPatients.aspx?EmployeeId=" + Name);
}
then on load event of next page
do something
protected void Page_Load(object sender, EventArgs e)
{ string Name= Request.QueryString["Name"];
this.txtPatientName.Text = Name;
}