What was the name of the last dog sent into space by the Soviet Union in 1960?

Zvyozdochka.

On the March 25th of 1961, the last dog-cosmonaut named Zvyozdochka (in translation from Russian: Little Star) completed a successful space flight. Her contribution to science gave the Soviet scientists enough confidence to start sending humans to space. Zvyozdochka was launched just a couple of weeks before the first human, Yuri Gagarin, stepped out to journey into the outer space.

https://leaderofthepackdogtraining.org/zvyozdochka-the-last-dog-in-space/

According to https://en.wikipedia.org/wiki/Soviet_space_dogs, there were two more dogs in space in 1966.

Veterok and Ugolyok were sent on a 21-day mission which they survived without lasting health issues, although they suffered from multiple short-term problems on their return.