<style>
    .split-button-container .k-button {
        border-right: 0;
        border-top-left-radius: 0;
        border-bottom-left-radius: 0;
    }

    .split-button-container .k-dropdown,
    .split-button-container .k-dropdown-wrap {
        border-left: 0;
        margin-left: -3px;
        border-top-left-radius: 0;
        border-bottom-left-radius: 0;
    }
</style>

    <div class="split-button-container">
        <TelerikButton Icon="@IconName.Star" OnClick="@SplitButtonClick">@GetSelectedActionText()</TelerikButton>
        <TelerikDropDownList Data="@myDdlData" TextField="MyTextField" ValueField="MyValueField"
                             Width="40px" PopupWidth="auto"
                             Value="@selectedValue" ValueChanged="@( (int v) => MyValueChangeHandler(v) )">
            <ValueTemplate>
                <span></span>
            </ValueTemplate>
        </TelerikDropDownList>
    </div>

@code {
    int selectedValue { get; set; }

    async Task SplitButtonClick()
    {
        Console.WriteLine($"split button clicked, selected value is: {selectedValue}, the selected text is: {GetSelectedActionText()}");
    }

    async Task MyValueChangeHandler(int theUserChoice)
    {
        Console.WriteLine($"Dropdown Changed: the user chose: {theUserChoice}");
        selectedValue = theUserChoice;
    }

    string GetSelectedActionText()
    {
        return myDdlData.Where(itm => itm.MyValueField == selectedValue).FirstOrDefault().MyTextField;
    }

    public class MyDdlModel
    {
        public int MyValueField { get; set; }
        public string MyTextField { get; set; }
        public string ExtraField { get; set; }
    }

    IEnumerable<MyDdlModel> myDdlData = Enumerable.Range(1, 20).Select(x =>
            new MyDdlModel
            {
                MyTextField = "item " + x,
                MyValueField = x,
                ExtraField = "more item info " + x
            }
        );
}