You need to have an id column for each row and pass it as parameter in to your query.
The current row id. in your table you may have a unique id for each row.
In grid view where you are having your edit button pass commandName as id
e.g
<asp:button id="btnEdit" text="Edit" runat="server" commandargument="<%#Eval("id")%>" commandname="Edit" xmlns:asp="#unknown" />
in grid view RowCommand event:
using(SqlCommand cmd = new SqlCommand("update dbo.RecordEmployee set TIME_OUT=@timeout, REMARKS=@editRemarks where EMPLOYEE_NAME =@empname and id=@id", conn))
{
cmd.Parameters.AddWithValue("@id", id);
cmd.ExecuteNonQuery();
}