Anemometer combines anemo- with -meter. Behind those pieces are Greek anemos, wind, and metron, measure.
This is a modern instrument name assembled from older material. The Greek roots are not an ancient name for the complete device.
Sources
- Merriam-Webster: anemometer
The definition identifies the measured phenomenon.
- Merriam-Webster: anemo-
The combining-form entry gives wind, Greek anemos, and anemometer as an example.
- Merriam-Webster: -meter
The noun combining-form history gives Greek metron; its definition and barometer example support the connection.
- Online Etymology Dictionary: -meter
Also built on *-meter* (from Greek metron "a measure"): barometer, odometer