If I use Judge Whistle and choose to put a "Judge" card from my discard pile into my hand, can I put a "Judge Whistle" into my hand?
No, that choice only allows you to put a card named "Judge" into your hand; it does not allow you to get a card "with Judge in its name".
Source: Team Up FAQ (2019-01-18), TPCi Rules Team (2019-01-31)

Relevant cards

Note: All applicable cards may not be listed below.
SM9_146
SM9_146
SM9_194
SM9_194