Satoshi Nakamoto is a pseudonym, and this entry makes no claim about who used it.
Two things were published under the name. The first is the Bitcoin whitepaper, Bitcoin: A
Peer-to-Peer Electronic Cash System, which Bitcoin Core still hosts at
bitcoincore.org/bitcoin.pdf. The second is the original Bitcoin client. bitcoin.org
records that the first specification and proof of concept was published in 2009 on a
cryptography mailing list under this name, and bitcoincore.org describes Bitcoin Core as a
direct descendant of that software.
bitcoin.org also records that Satoshi left the project in late 2010 without revealing much about himself, and notes that the person did not control Bitcoin: changes since then have come from a large number of other contributors, under the same open review process anyone else is subject to.
Who used the name is not known, and this directory does not speculate. A pseudonym is a stated preference, and guessing past it is not research. Every claim above is about published work, which is the only thing there is a record of.