What should put in the license field of package.json if my code is only for use by the company I work for?

UNLICENSED is now a valid license option in npm. This is not the same as "The Unlicense".

at the time of writing UNLICENSED (see the code sample in the question) was not an option please see jcollumns answer

Adding private to package.json will help:

"private": true

On the second column of the table found on this link, https://spdx.org/licenses/, you can see all the different SPDX format to used in your package.json.

The name of the column is Identifier just in case. Thanks and hope it helps.