Is it permissible to publish Islamic thoughts under the author's name, and is that considered showing off (riyaa'), and does not mentioning the name increase the reward?

Thoughts and ideas are presented to the Qur’an, the Sunnah, and scholars. What is correct is disseminated, and its doer is rewarded, and what is wrong is reconsidered. Some scholars, like Ibn al-Jawzi and Ibn al-Qayyim, used to write their thoughts. Ibn al-Qayyim explained that thoughts and obsessions are of three types: divine (Rahmaniyah), satanic, and self-originated (Nafsaniyah). He also stated that infallibility is for Messengers only, and that others may be right or wrong, and that what is cast into hearts should not be heeded unless it is presented to what the Messenger brought and attested to its conformity. As for writing one's name on thoughts, it is not necessarily ostentation (riya’). The writer may intend fame, or to introduce himself, or to communicate with readers. It is better to write one's name on an article so that people accept what is written, and so that a person strives for his work to be purely for Allah the Almighty.