[SpiralChiral (OP)]

How was Linnaeus able to name so many species?

[Chemistry4me]

He had a lot of spare time?

[Don_1]

Linnaeus used a system of sexual reproduction organs to determine species families.

Flowers with 1 female & two male staman fall into one category, 2 female & 3 male another and so on.

In fact John Ray had already devised a better system of placing species into groups and had identified a great many species.

[Tomassci]

Linnaeus "getted" many species from the world scientists.

[evan_au]

Because his students traveled the world looking for new species.

One was Daniel Solander, who traveled with James Cook on his round-the world expedition to exotic places like Tahiti, New Zealand, New Guinea and Australia which had rarely been visited by a trained botanist.
See: https://en.wikipedia.org/wiki/Daniel_Solander

[alancalverd]

He didn't, any more than Rowland Hill wrote lots of letters. He simply invented a system by which other people could do it.