The following snippet below describes on how we are going to set the ListItem Background Color based on the Color name displayed in the DropDownList


ASPX MARKUP OF DROPDOWNLIST

<asp:DropDownList ID="DropDownList1" AppendDataBoundItems="true" runat="server" AutoPostBack="True" OnSelectedIndexChanged="DropDownList1_SelectedIndexChanged" OnLoad="DropDownList1_Load">
        <asp:ListItem Value="-1">Select</asp:ListItem>
        <asp:ListItem Value="0">Red</asp:ListItem>
        <asp:ListItem Value="1">Blue</asp:ListItem>
        <asp:ListItem Value="2">Green</asp:ListItem>
        <asp:ListItem Value="3">Violet</asp:ListItem>
</asp:DropDownList>

RELEVANT CODES
protected void DropDownList1_Load(object sender, EventArgs e)
{
        for (int i = 0; i < DropDownList1.Items.Count; i++)
        {
            DropDownList1.Items[i].Attributes.Add("style", "background-color:" + DropDownList1.Items[i].Text);
           
        }
}

That's it!