Questions about business logic layer and data access layer in a project

I would separate the BLL from DAL as a best practice. I interact between BLL and DAL via interface. Example:

public interface IProductRepository
{
    void Add(Product myProduct);
    Product Get(string name);
    Product GetById(int id);
}

where business object Product is:

public class Product
{
     public int Id { get; set; }
     public string Name { get; set; }
     public decimal Price { get; set; }
}

The BLL class is:

public class ProductManager
{
     private readonly IProductRepository productRepository;

     public ProductManager(IProductRepository productRepository)
     {
          this.productRepository = productRepository ?? throw new Exception("message");
     }

    public void AddProduct(Product myProduct)
    {
        try
        {                  
            // Here code validation ecc....

            // Add product to database
            productRepository.Add(myProduct);
        }
        catch(Exception e)
        {
            // Handle exception  
        }
    } 

    public Product GetProduct(string name)
    {
        try
        {
            // Here code to validation ecc....

            // Get product from database
            var product = _productRepository.Get(name);

            return product;
        }
        catch(Exception e)
        {
            // Handle exception  
        }
    }
     // ecc ecc
}

where DAL (i would use Entity Framework) is:

public ProductRepository : IProductRepository
{
    public void Add(Product myProduct)
    {
        using(var dbContext = MyDbContext())
        {
            var dbProduct = new PRODUCTS
            {
                NAME = myProduct.Name,
                PRICE = myProduct.Price
            }

            dbContext.PRODUCT.Add(dbProduct);

            dbContext.SaveChanges();
        }
    }

    // ecc ecc
}

Now I have some questions: - Is this the correct implementation? - If I want insert a product but I want to check if a product with the same name is on db, do I first call the Get method in BLL and then call Add method (the db context is open and closed each time, is an overload?) or I can insert logic in DAL like:

var dbProduct = dbContext.PRODUCTS.FirstOrDefault(p => p.NAME == name);

if(dbProduct == null) .... // insert else throw exception 

In the latter case, however, if a change the dal the bll logig would no work anymore. -Is it right to use EntityFramework in this way, or do I lose all the benefits of linq? Sorry, but i'm very confused.

Thank you.