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The two largest craters on Mercury are names Caloris (meaning "hot") and Rembrandt (for the painter). So there doesn't seem to be a pattern.

By convention, craters on Mars are named for people who studied the planet (like Cassini) or wrote about it (like Bradbury).

Is there a similar naming convention for the craters at the surface of Mercury?

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    $\begingroup$ Just a note that your second paragraph is incorrect via incomplete information: Only craters >50 km fit into the naming scheme you wrote. Smaller craters on Mars are named after small towns and villages. planetarynames.wr.usgs.gov/Page/Categories . That page also gives the themes for all features on all bodies for which a system has been established, including Mercury craters. $\endgroup$
    – Stuart Robbins
    Feb 8, 2021 at 19:37

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A quick search returns that wikipedia has an extensive list how different things are named on various celestial bodies.

For Mercury's craters it quotes "Famous deceased artists, musicians, painters, authors". As source of its wisdom it gives the IAU working group on planetary system nomenclature as authoritive source for them - the source which decides on official naming.

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