Is seeking knowledge to dispel ignorance and for self-cultivation, rather than for people's praise, considered showing off (riya')? And what is the virtue of memorizing a new hadith?

Learning knowledge with the intention of removing ignorance from oneself is not hypocrisy (riya'), as Imam Ahmad said. Similarly, the intention to learn knowledge to avoid speaking about Allah without knowledge is a good intention and is not considered hypocrisy, because speaking about Allah without knowledge is one of the greatest prohibitions. As for memorizing hadith, the Prophet, peace and blessings be upon him, said in its فضl (virtue), as narrated by Zayd ibn Thabit: "May Allah illuminate the face of a person who hears a hadith from us, memorizes it, and conveys it to others."