The answer to your question is that, unless you received an actual W-2 from the National Institutes of Health, you won't want to enter this income under the regular W-2 TurboTax interview (which it seems like you are attempting to do, given that you ask about an "employer name" and EIN "number".)
Instead, you will enter this income on your tax return somewhat differently. While it is certainly still taxable income, a grant like this is not wage income, nor is it subject to Social Security or Medicare taxes.
For more details and a discussion, please refer to the following AnswerXchange posts:
https://ttlc.intuit.com/questions/3726385
https://ttlc.intuit.com/questions/3840431
The information found there will also show you how to (correctly) enter your NIH T32 grant income into TurboTax, which will then ultimately appear on your personal tax return.
Thank you for asking this question; and good luck with your future professional activities.
