Although stipends are not considered salaries, these funds are subject to federal and, sometimes, state income tax. Such income may be reported by the sponsoring institution on IRS Form 1099, Statement of Miscellaneous Income. Often, the business office of a sponsoring institution will annually prepare and issue IRS Form 1099 for fellows paid through the institution.
That said, it’s a question best discussed with your institution and your tax preparer.
Read Section 11.2.10.6 Taxability of Stipends of the NIH Grants Policy Statement for additional context. Learn how fellowship funds may be spent at What Do Training Funds Pay For?