No, this isn't something you can choose to do, unfortunately. If you acquire this painting at the auction, your choices are, from the wiki page for the Van Rogh painting:
If you gained the necessary information from Yaromir by correctly answering his question, buying the painting would later start the Avid Collector quest in which the painting can be sold on to Marcus T.K. Hodgson, a famed Novigrad book dealer, who will pay quite a tidy sum for it.
Alternatively, Geralt can hold onto the painting and display it at Corvo Bianco with the Blood and Wine expansion installed.
So you can either sell it for quite a bit or put it on display at Corvo Bianco, but you can't give it to
like you want to.