Is it obligatory for someone who has taken money wrongfully to go to its owner and inform him of that and disclose his identity, or is there another way to return the money without exposing himself, especially if a long time has passed since then?

What you take in gratuities for completing tasks, and your taking from what you were entrusted with to deliver to workers, is unlawful (haram). You must return what you took to its owner, even if through indirect means. As for throwing the money in a garden, that is not sufficient. What is required is to deliver the money to him in such a way that he can take it and knows it is his money.