In his tafsīr of “I am putting a caliph on the earth” [2:30], Imam Qurtubi refutes the claim by the Shi‘ites that the Messenger of Allah ﷺ specifically named someone to rule after him as caliph:

“The proof of the absence and non-existence of a text of designation naming a specific imam is that, if the Prophet ﷺ had imposed on his community obedience to a particular imam so that it would not be possible to turn away from him to someone else, that would have been known since it is impossible to obligate the entire community to obey Allah in something which is unspecified and when there is no way to know that obligation. Since knowledge of who he is is mandatory, then that knowledge must come by way of multiple transmission which necessarily demands that it be known or deduced, or that it come from single reports. It is not possible for that to have the same authority as multiple transmission which demands a priori knowledge or by evidence, since if that had been the case, every responsible person would find in himself knowledge entailing obedience to that specific person and that would be part of the dīn of Allah which is obliged for him, just as every responsible person knows from the dīn of Allah what is obliged for him regarding the five prayers, fasting Ramadan, ḥajj and the like.”

[Abu ‘Abdullah Muhammad ibn Ahmad al-Qurtubi, Tafsīr al-Qurṭubī: The General Judgments of the Qur’an and Clarification of what it contains of the Sunnah and Āyahs of Discrimination, Vol. 1, translated by Aisha Bewley, Diwan Press, 2019, p. 150]