No, alimony is not reported on the form 1099-NEC. The form 1099-NEC form is being used to report nonemployee compensation (contractor compensation).
You would continue to use the form 1099-MISC and reported it on box 3 (Other Income).
Be aware that the tax laws changed as to the reporting of alimony in 2017, but if you have been reporting alimony this way prior to the law change the law wouldn't change your reporting requirements.
For more information on this please read IRS Topic 452.