Being remembered implies memory carried through time and space. Being remembered implies future humans remembering.

The grand scheme of the cosmos makes it questionable. There'll be no human being millions of years from now, at least not the humanity that we know of. If humans lasted for the next thousand years, it'll certainly be a cosmic miracle, because the scientific tendency is a mass extinction event for the foreseeable future (due to factors such as climate change).

We don't need to try and imagine a foreseeable future. We can look at the past and question ourselves whether it's possible or not for a person to actually be remembered. Do we know and remember the name of that first person to ever write within language rules, possibly a Sumerian person? Do we know and remember their name, their life, how they looked like, what they ate? What about the first person to ever lit a fire, possibly a hominid? What about the first person to make something that resembled a wheel?

Time's cruel. I mean, there's no cruelty as in a human sense, it's simply a great, ineffable cosmic indifference towards the "order out of chaos" that we call "living beings". Even when there are memory carriers, people who remember other people, the memories and thoughts they carry will fade into the oblivion of the entropy. It's how cosmos functions. Order came from the primordial chaos, and to the primordial chaos it must return.

So, how do I want to be remembered? Do I ever want to be? Even if I did want to be remembered, it wouldn't matter, because all matter and energy will be forgotten amongst the cosmic soup of chaos rearranged by an unstoppable entropy.