Canon wise (and officially) he only has one and that's Kiara. Apparently according to the disney folks who made SP Kiara is also the cub at the end of TLK.
Before SP was made the cub was termed as ''Fluffy'' by the staff...after all, they didn't plan on making a sequel.
Then during the period between '94 to '98, a different 'faction' invented Simba's cub Kopa in the Six adventures.
During pre production (ie: story boarding etc) the designers planned to have two cubs for Simba: Aisha/Kiara/Shani (but this name is a bit sketchy in origin) and Chaka. Yet they dropped Chaka from production like Meethu, Bhati etc and had only Kiara.
So thus, Kiara is the official cub of Simba and Nala.
Personally, I make Simba and Nala have two cubs; Kiara and Kopa. Although I have had some ideas of including Chaka who from 'designs' would have a mixture of Simba and Nala's colouring or Nala's eye colour or something.
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Forgot to add. There are lots of additional cubs of Simba and Nala through fan theories. One widely known is Tanabi.