In my experience this is more important at large companies, because your work is more likely to get lost in the noise. At startups work is often much more visible and perhaps there's less of a need for this, but not a bad idea to do it either way and you can KISS, ask for a quarterly check-in with your manager to go over your work accomplishments, ask for feedback, etc;

If people don't already know what you're doing at a startup, then you have REALLY chosen the wrong startup!

I have no doubt that the LinkedIn addicts and self-help book cultists will swoop down to insist that this advice applies to all companies. But really, it is most heavily tilted toward tech giants and large enterprises.