"This mission will answer questions scientists have sought to uncover for more than six decades," said Zurbuchen.
Understanding the Sun has always been a top priority for space scientists.
Studying how the Sun affects space and the space environment of planets is the field known as heliophysics.
The field is not only vital to understanding Earth's most important and life-sustaining star, it supports exploration in the solar system and beyond.
Submission of names will be accepted until April 27, according to the US space agency.
The spacecraft, about the size of a small car, will travel directly into the Sun's atmosphere about four million miles from the star's surface.
The primary science goals for the mission are to trace how energy and heat move through the solar corona and to explore what accelerates the solar wind as well as solar energetic particles.
The mission will revolutionise our understanding of the Sun, where changing conditions can spread out into the solar system, affecting Earth and other worlds.
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