Generally speaking, this is fine. I'm not sure how PR might be different, but most states have a way to register a Doing Business As on the secretary of state's web site. You should do this if PR permits it.
Also, if your non-profit has a tax-exempt status, then you need to be careful to make sure all activities under both names are consistent with the exempt purpose of the organization. Income unrelated to the exempt purpose (subject to some exceptions) is taxable, and too much unrelated business income can threaten the tax exempt status.