Though your approach is a little bit unclear right now (for e.g. we don't know which entities you are trying to update), however you can modify your code like this,

public void updateShoes(Shoe shoe) 
{
    var query = from b in db.BrandTbls.AsQueryable()
            join m in db.ShoeModelTbls on b.BrandID equals m.BrandID
            join s in db.ShoeTbls on m.ModelID equals s.ModelID
            where shoe.ShoeID == s.ShoeID 
            orderby m.ModelName
            select new 
            { 
                Shoe = shoe, Brand = b, Model = m
            };
 
    foreach(var o in query)
    {
        o.Shoe.ColorName = "Black";
        o.Brand.BrandName = "New Branding";
        o.Model.ModelName = "Something else";
    }
 
    db.SaveChanges();
}

Rather picking selected properties from each Entity, you can pick whole entity. Then you can update each entity in a loop as I have doing above.