Your problem begins and ends with statistics and estimates. I have reproduced your situation on my servers and found some interesting hints, and a workaround solution.
First things first, let's take a look at your execution plan:
When a view is used we can see that a filter is applied after the Remote Query is executed, while without the view there was no filter applied at all. The truth is that the filter was applied inside the Remote Query, at the remote server, before retrieving the data over the network.
Well, obviously applying the filter at the remote server and thus retrieving less data is a better option, and obviously that only happens when not using a view.
So... what is so intersting...?
Surprisingly, when I changed the filter from cognome = 'test' to cognome = N'test' (unicode representation of the string) the view used the same execution plan as the first query did.
I guess the reason is that somehow when using the view SQL Server estimated that there will be a small number of rows returning from the (remote) query, and that a local filtering will be cheaper, but when SQL Server had to implicit convert NVARCHAR to VARCHAR, statistics could no longer be used and the decision to filter locally was not taken.
I have looked for the statistics locally, but the view had no statistics, so my guess is that the view uses the remote statistics in a way that ad-hoc query does not, and than takes the wrong decision.
OK, so what solves the problem?
I stated earlier that there is a workaround (at least until someone comes up with a better solution), and no, I don't mean using unicode for your strings.
I wanted to give an answer first, I still have to find why, but when using an Inline Function SQL Server behaves exactly the same as with the query (without view), so replacing the view with the function will give the same result, in a simple query, and with good peformance (at least in my environment).
My code suggestion for you is:
CREATE FUNCTION fn_anagrafiche2()
RETURNS table
AS
RETURN
(
SELECT *
FROM dolph2.agendasdn.dbo.vistaanagraficagrp
UNION
SELECT *
FROM dolph2.acampanet.dbo.vistaanagraficagrp
UNION
SELECT *
FROM municipio2.dbnet.dbo.vistaanagraficagrp
)
GO
The query will then be:
SELECT *
FROM fn_anagrafiche2()
WHERE cognome = 'prova'
This works on my servers, but of course test it first.
Note: I do not recommend using SELECT * at all, as it is prone to future errors, I simply used it because it was in your question and there was no need for me to change that when I can add this remark instead :)
Best Answer
Scalar UDFs always affect performance. What you might have read is that you probably don't want to use them in your WHERE or JOIN ON clauses because that test is happening as part of the filtering stage and thus may force every single row to go through the UDF to determine the output.
This is compared to the less worse option of just using it in the part of the SELECT statement that specifies the columns/data you want to return; in which case you've already filtered everything and so there's presumably less to work on. i.e. Doing a test of the filtered data to return a bit field as to whether there's a match or not.
Apart from this, about making searches more performance, in your case you are searching for a string anywhere within another string, and that's bad. To make things faster you would need to make it so that you are only searching for a string at the beginning of the string (x like '%...') or end of the string (reverse(x) like ('%' + reverse('...') as a persisted computed column and then stored in an index).
Either way you would then go with dynamic SQL; iterate the temp table and build up a string with the SQL statement you want that codes in the specific search terms you are looking for in the WHERE clause; then run with sp_executesql. But it's terrible practice and sometimes a security nightmare.
But it would only go significantly faster if it's on those '%...' searches. Not '%...%'.
The other alternative is to investigate full-text indexing to see if your specific search terms are going to meet that criteria, but it's much more complicated, and you're going to have to crack open a book to learn it.