The name 'tricorder' relates to its three main functions (sensing, computing and recording) and is, according to the Star Fleet Medical Reference Manual, considered quasi-canon but written by Geoffrey Mandel, senior production artist and designer for TNG, DS9 and Voyager, an abbreviation of the device's full name:
"TRI-function reCORDER"
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/pipYR.png)
This is further backed up by the reference on tricorders in the (fully canon) Star Trek TNG Technical Manual
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/rny32.png)
and a similar description in the Voyager Technical Manual
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/dImm0.png)
and a similar description in the DS9 Technical Manual
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/67oYj.png)
and a similar description in the TNG Writer's Technical Manual
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/WDPIw.png)