Waswas
Waswas (in Arabic وسوس) in Islam is a term for "whispers from Shaytan". When a Muslim has some thoughts against Islam, he disregards them as waswas - a voice of Shaytan.
Waswas in the Qur'an
The Arabic word وسوس (waswas) in various forms appears 5 times in the Qur'an.
The first two refer to the story of Adam and Eve. The fa- prefix means "but" or "then".
Then one time it's a persons soul which whispers. The tu- simply indicates present tense, 3rd person, feminine, singular verb.
And two times in a short sura 114. The al- indicates definite article (before a noun). The yu- indicates present tense, 3rd person, singular, masculine verb.
114:1 Say: I seek refuge in the Lord of men,
114:2 The King of men,
114:3 The god of men,
114:4 From the evil of the retreating whisperer (ٱلْوَسْوَاسِ, al-waswasi)
114:5 Who whispers (يُوَسْوِسُ, yuwaswisu) into the hearts of men,
114:6 From among the jinn and the men.
Tafsir Al-Jalalayn says that the "whisperer" in 114:4 is Satan:
From this we can conclude that the concept of waswas (Satan whispering into Muslim minds) is described in the Qur'an, so it is definitely a part of the Islamic doctrine.