It's not the same as actually going of course but NASA are offering to take your name on a flash drive into space aboard Artemis I's uncrewed Orion test flight and fly it around the moon.

You only need to provide your name and set a pin code.

Orion is currently scheduled to launch in May.

[ Main Image: Orion. Credit: NASA via YouTube. ]

References

NASA. Artemis I. (viewed March 5, 2022)

NASA. Artemis I - Fly your name around the Moon! (viewed March 5, 2022)

NASA (April 8, 2021). Artemis I: NASA’s Plans to Travel Beyond the Moon. YouTube.

NASA (September 21, 2021). Priming NASA's Artemis I for Launch to the Moon. YouTube.

Wikipedia. Artemis 1. (viewed March 5, 2022)