Yes, you can -- and there are a few ways to do it. You may simply want to hand off a series of notes for someone else to transform into a eulogy and/or obituary. On the other hand, you may want to write the entire eulogy or obituary on your own. Some people even write these collaboratively with their friends or family, particularly when they have a terminal diagnosis.
There are some benefits to preparing an obituary or eulogy in advance of your death. For one, you'll feel more confident about how it will be written and who will write it. Also, it can give you more time to make sure that your loved ones know about your wishes.
When writing an obituary, there are kinds of information that you could include depending on the situation. Some people may want to include a list of their accomplishments or awards, while others may want to mention their favorite hobbies or interests. Writing out notes about your life can be a meaningful process for you, individually, or for you and your loved ones.