Do I need to get a COVID-19 test when flying from Italy to the Netherlands?

Yes, you do need a Covid test. Depending on the time between taking the test and arriving in the Netherlands, you might actually need two. According to government.nl:

If you are aged 13 or over and travelling to the Netherlands from a high-risk country, you must provide proof that you have tested negative for COVID-19. You can do this by presenting a negative NAAT (PCR) test result based on a sample collected no more than 24 hours before boarding the aircraft or ferry. Or you can present both a negative NAAT (PCR) test result based on a sample collected no more than 72 hours before arrival in the Netherlands and a negative rapid test result based on a sample collected no more than 24 hours before boarding. A negative rapid test result is not mandatory if you are travelling to the Netherlands by car, coach or train.

The Dutch government provides a list of testing locations in Italy. I think these are just recommended locations, but you may also want to check the requirements on how the testing results are reported. These requirements are:

The negative test result must be in English, German, French, Italian, Portuguese, Spanish or Dutch. A translation of the test result will be accepted provided the translation bears the original signature or stamp of the doctor or institute that conducted the test.

The document must include the following information:

• Type of test: the test used must be a molecular NAAT (PCR) test (either PCR, RT PCR, LAMP, TMA or mPOCT). No other type of test, including antigen tests and serological tests (blood tests to detect antibodies), is valid;
• Test result: the test result must be negative (or ‘not detected’);
• Your given name and surname as stated in your passport;
• Date and time you were tested: the test sample must have been collected no more than 72 hours prior to arrival in the Netherlands;
• Name and contact information of the institute or laboratory that conducted the test.