Good old Steen and Seebach discuss the Smirnov deleted sequence topology in their Counterexamples in Topology (2nd ed. 1978).
This is also reported as the $K$-topology, in e.g. Wikipedia etc.
However, none of the sources that I've found tell us which particular Smirnov is behind it.
I am guessing it's Yurii Mikhailovich Smirnov as of all the Smirnovs I know of in mathematics, he is the one who has greatest involvement in topology.
(For example: Vladimir Ivanovich is known for a 5-volume textbook, and Nikolai Vasilyevich made a name for himself in statistics.)
Yurii Mikhailovich is of course the mathematician whose name is associated with the Nagata-Smirnov metrization theorem, so it's more than plausible it's the same one.
Can anyone point me towards a source that can confirm this?
It is Yurii Mikhailovich Smirnov: the space is Example $1$ in his paper О МЕТРИЗАЦИИ ТОПОЛОГИЧЕСКИХ ПРОСТРАНСТВ (On metrization of topological spaces), Uspekhi Matem. Nauk, 1951, 6, 100-111. It’s on p. 107 at the end of Section 2.