For pure prestige and badassery reasons, the first supercarriers should obviously be Beijing, Shanghai, Guangzhou and Shenzhen.
Wait.. if you were going by municipalities then they should be : Beijing, Chongqing, Shanghai, Tianjin.
That would be cool, too.
Technically speaking, the 003 Fujian is already a supercarrier.
Although, I disagree naming Chinese flatdecks after Chinese municipalities.
Despite Beijing, Shanghai, Tianjin and Chongqing are categorized as municipalities, and are thus at the same rank as provinces and autonomous regions - In the end, they are still very much cities by nature. So I don't think naming Chinese flatdecks after these municipalities is a good idea.
Speaking of which, one of the 051-class destroyers that intercepted the Soviet battlecruiser Frunze in 1985 is named after Chongqing.
Moreover, there are the matters of wartime prestige and morale.
We have already witnessed the blow to Russian morale (to at least a certain degree) when Moskva was sunk by Ukrainian Neptune anti-ship missile in April last year. This is considering that:
1. Moskva is a cruiser;
2. Moskva is the flagship of the Black Sea Fleet;
3. Moskva is the most powerful warship in the entire Black Sea (hence #2); and
4. Mosvka is named after Moscow, which is the capital city of Russia and also the most important city across all of Russia.
Speaking of cruisers - Yes, I think the Moskva (and the Slava-class in general) can be considered as capital ships of the Russian Navy, based on the present (dilapidated) state of the surface fleet of the Russian Navy.
But for the PLA Navy, China's ability to build multiple cruiser-sized surface combatants at once has basically resulted in the 055 large destroyers/"cruisers" being considered as normal surface combatants, similarly to their smaller cousins i.e. the 052D destroyers. Therefore, in my opinion, the title of "capital ships" in the PLA Navy should be reserved for CVs and LHDs.
Therefore, if the sinking of Moskva can already bring such negative effects to the Russian war effort and morale in Ukraine, what do you think would happen if the news broke that the Chinese CV Beijing or the Chinese LHD Shanghai has been sunk due to enemy action?
Based on my personal preferences, if the names from the municipalities are to be used on PLAN warships, the 055 large destroyers and/or their successor class of "true" cruisers (maybe 055A/B) with more VLS cells, railguns and DE-CIWS than the present 055 would be more fitting.