When I throw a rock into water, ripples are formed. If I throw a rock into a black hole, will there also be ripples?

Yes, although they would be very small.

The closest example we have is not something falling into a black hole, but a neutron star orbiting about another neutron star. This is the double pulsar discovered by Taylor and Hulse. And it emits gravity waves.

In a similar way, anything falling into a black hole will be accelerated, cause an acceleration of the black hole, and that acceleration will cause emission of gravity waves.

There is nothing special about a black hole that makes this answer any different from what you get by falling into any object.

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