Hi Destinykid,
Using below article i have created the example.
You need to use Contains method in where clause.
Check this example. Now please take its reference and correct your code.
Controller
public class HomeController : Controller
{
    private DBCtx Context { get; }
    public HomeController(DBCtx _context)
    {
        this.Context = _context;
    }
    public IActionResult Index()
    {
        List<Customer> customers = this.Context.Customers.Take(10).ToList();
        return View(customers);
    }
    [HttpPost]
    public IActionResult Index(string name)
    {
        List<Customer> customers = this.Context.Customers.Where(x => x.ContactName.Contains(name)).ToList();
        return View(customers);
    }
}
View
@addTagHelper*, Microsoft.AspNetCore.Mvc.TagHelpers
@using EF_Core_MVC.Models;
@model IEnumerable<Customer>
@{
    Layout = null;
}
<!DOCTYPE html>
<html>
<head>
    <meta name="viewport" content="width=device-width" />
    <title>Index</title>
</head>
<body>
    <form asp-controller="Home" asp-action="Index" method="post">
        <input type="text" name="name" />
        <input type="submit" value="Submit" />
    </form>
    <hr />
    <table cellpadding="0" cellspacing="0">
        <tr>
            <th>CustomerID</th>
            <th>ContactName</th>
            <th>City</th>
            <th>Country</th>
        </tr>
        @foreach (Customer customer in Model)
        {
            <tr>
                <td>@customer.CustomerID</td>
                <td>@customer.ContactName</td>
                <td>@customer.City</td>
                <td>@customer.Country</td>
            </tr>
        }
    </table>
</body>
</html>
Screenshot
