The full company enters through the house singing the question that will be asked throughout the whole show ("What's in a Name?"). The audience is prompted to consider the significance of their own names and if changing their names would effectively change who they are. Brandon is singled out. An aspiring astronaut, he's convinced that he must change his "dumb" name to realize his dream. Lights reveal a portion of the Space Center at NASA, where Brandon is among a class being toured through the exhibit. Estrella, a youngster newly arrived from Guatemala, is also compelled by the space module, but her limited English capability keeps her quiet until she admits to Brandon how awkward she feels ("Spanglish").

Brandon and Estrella rejoin the group. Brandon seems to know more than the tour guide, but, when the Guide gives him the chance to lead the tour, he flounders. The tour ends. Everyone starts moving off, and we hear a door close. Brandon emerges from the other side of the space capsule to find everyone gone. Mesmerized by the display, he fantasizes about flying on a real spaceship someday ("To Be an Astronaut"). A mission control voice calls to him, and he's awakened from his trance. He tries a door. It's locked. Estrella is heard off in the distance. She joins him on stage, and the pair, who have forged a connection, try to figure out how to escape. Unfazed by the urgency of the situation, Brandon complains about his name again, but Estrella explains that changing his name won't change his fate ("When You Find Your Star").

The two friends decide to wait for someone to find them. Brandon hits a switch on the wall. Immediately, a field of stars comes up on a projection screen. Overwhelmed and excited, Brandon coaxes a reluctant Estrella into exploring, since they are bound to be stuck there for awhile. Brandon opens the capsule, revealing its interior. An effigy of an astronaut sits at the pilot's position. They are in awe. Brandon sits in the adjacent seat and pretends to take command. Suddenly, the wax figure beside him begins to move and come alive. Estrella is somewhat freaked, but Brandon is game, willing to go along for the ride. The Astronaut informs Brandon of their all-important mission to the Blue Planet – there are major problems there that only he can solve. The Astronaut then tests Brandon's knowledge about space ("Sing a Song of Planets"). Estrella eventually joins in. Without thinking, Brandon punches several buttons. To his great surprise, lights suddenly pop up on the control panel and the clear sounds of power are heard. The Astronaut calls for a countdown ("Beyond Pluto"), as Brandon and Estrella have completely submitted to the fantasy.

All is totally silent, and they seem to be floating among a blanket of brilliant stars. As the three travelers discuss their imminent mission, the ship shakes violently. The Astronaut assures them that they've just entered the Blue Planet's gravitational field. Brandon pushes a series of buttons at random, and the ship suddenly slows and descends to a landing. The module lands gently, and all is quiet. A group of Blue Planetarians surrounds the ship as the three exit the craft. The Planetarians suspiciously mutter. Brandon (now referred to as Commander Deke Aldrin Atwater) tells the nameless Planetarians that he has come to save them. The Astronaut confirms that Brandon will help them get their names back, names that are being held captive by the terrible Wizard of Ahhhs. The wizard was driven off to a far distant place due to his constant stammering. He consequently used his magic to make the Planetarians forget their real names ("The Blue Planetarian Blues").

Brandon learns that the names are kept in a chest that the wizard has buried deep underground. Encouraged by the Astronaut, Brandon (believing that the name, Deke, has given him power) promises to rescue the names. The Astronaut stays with the citizens of the planet as Brandon and Estrella set forth, via an odd-looking transporting machine, on their journey to the far north.

There is a flurry of darkness, light and sounds, and then... all is quiet. We can see a blue structure of solid ice that somehow resembles a palace. They gingerly exit the transporter and are greeted by a huge, echoing voice ("The Wizard of Ahhhs"). Displeased with their trespassing, the Wizard freezes Estrella. As Brandon struggles to move Estrella, he pushes a stalagmite of ice, revealing a bedraggled old man with a microphone, before a panel of lights and dials. Brandon confronts the old man and demands that Estrella be released. He obliges and then introduces himself as Reginald Sylvan Armbruster, the Third. The "wizard" also agrees to return the names of the citizens, but, unfortunately they are at the bottom of a mine shaft, which collapsed some 150 years ago... and Blue Planet dirt is as hard as concrete. Brandon thinks that the transporter can get them to the chest. They all climb in, and Brandon takes over. He instinctively starts the engine. The ship takes off, and they move into sounds and speeding lights.

We hear the sound of a straining engine, then total silence. As the lights come back up, we are deep in the earth. They all get out, and the Wizard spies the chest. He races to it, opens it and removes the names inside. Once they've retrieved the treasure, they return to the transporter. Brandon starts the engine, but to no avail. Admitting defeat, the Astronaut appears... well, at least in Brandon's mind. He advises Brandon that the answer is in his name. The image disappears as Brandon tries to figure out what he meant ("Finding Their Names"). He figures out that he must name the transporter – he dubs it Angelica – and a welcoming roar suddenly issues from the machine ("Hooray!"). They clambor into the ship. There's a rush of sound and light, and they're off! Everything slows and settles, and we're back on the Blue Planet City. They all stand outside the ship as Brandon hands out the placards to a cheering throng; the blue citizens transform into their "true" appearance ("Blue Planetarian Transformation"). The Planetarians apologize to the Wizard, and the Astronaut informs Brandon and Estrella that it's time to go home ("Beyond Pluto – Reprise").

Lights fade to black for a moment. Lights fade up. We are back at the Space Center, with Brandon gripping the controls of the space module. Offstage voices shout to Brandon and Estrella. They get out of the module and then look back at it as Brandon realizes that he is proud of his own name ("Finale").