LinqPad8 is showing me a cached Entity ?

I'm guessing this is Linq2Sql caching the entity.

There are a number of ways to resolve this.

If you are not going to be calling SubmitChanges() then you can disable the tracker and caching at the start of your query.

this.ObjectTrackingEnabled = false;

Alternatively keep a reference to the customer that will be changed outside LinqPad, and then refresh that record after calling your webservice - e.g.

var customer = Customers.Single(s => s.CustomerIdInDataHost == _oldCustomerID).Dump();

// ASMX webservice that simply replace the customer id for the Entity (same database as used in my Query)
_dataHostService.ReplaceCustomerIdInDataHost(_datahostapikey, _owner, _newID, _oldCustomerID);

// Refresh the customer record
 this.Refresh(System.Data.Linq.RefreshMode.OverwriteCurrentValues, customer );

// Show the updated Customer with the new ID
Customers.Single(s => s.CustomerIdInDataHost == _newID).Dump();

Alternatively you can create a new DataContext. Unfortunately you can do re-assign the new context to this, but you can something like

var dc = new TypedDataContext(this.Connection.ConnectionString);

dc.Customers.Single(s => s.CustomerIdInDataHost == _newID).Dump();

That is kinda dangerous as it is very easy to forget to prefix your query with dc.

Finally, Linq has a method to clear the cache but unfortunately it is marked as private, but you can if you use Uncapsulate, e.g.

var customer = Customers.Single(s => s.CustomerIdInDataHost == _oldCustomerID).Dump();

// ASMX webservice that simply replace the customer id for the Entity (same database as used in my Query)
_dataHostService.ReplaceCustomerIdInDataHost(_datahostapikey, _owner, _newID, _oldCustomerID);

this.Uncapsulate().ClearCache(); 

// Show the updated Customer with the new ID
Customers.Single(s => s.CustomerIdInDataHost == _newID).Dump();