If you want one dropdown for the entire view, then you wouldn't add the list to PaymentsViewModel, as that would be adding a dropdown for each payment. Also this viewmodel should have a singular name because each represents a single item: PaymentViewModel.
Payments.cshtml
@model PaymentsViewModel
@Html.DropDownFor(... Model.Merchants...)// select into ListItems
<table>...
foreach(PaymentViewModel payment in Model.Payments)
...your existing "grid"
PaymentViewModel.cs
public int PaymentID { get; set; }
public string Merchant { get; set; }
PaymentsViewModel.cs
List<MerchantsViewModel> Merchants {get;set;}
List<PaymentViewModel> Payments {get;set;}
Alot of how I would go about this depends on what you are trying to accomplish with this dropdown though.