This is a complex question. The United States does allow dual citizenship, and they will recognize it when you become a US citizen. However, the eligibility requirements are not the same in every country.
Your home country may not recognize your status as a U.S. citizen when you are on their soil. In extreme cases, there are countries that will terminate your citizenship if you apply for citizenship in the United States and complete the process.
That being said, familiarizing yourself with your country’s laws and finding a citizenship lawyer who offers free immigration consultations can be extremely helpful, especially when educating yourself on dual citizenship qualifications.