Nostr is freedom technology, not a technology build for private communication. Nostr is far from private, the content you share is public by default (there are some exceptions).
Text notes (kind 1) are wrapped in events which are defined regular:
for kind n such that 1000 <= n < 10000, events are regular, which means they're all expected to be stored by relays.
And with "stored by relays" this means stored permanent. Nostr does not provide a way to update or delete the content related to these kinds. Anyone can fetch those events with content.
When you update your profile, you will publish a new event with updated content. Relays are fetching the newest event with this kind (kind 0), and you should consider the following (this is a quote from NIP-01, you should read it): A relay may delete older events once it gets a new one for the same pubkey.
Always keep in mind every event you publish could be on the internet forever. It all depends on the behaviour of relays.
This is a good read from hodlbod if you would like to dive a little deeper: https://blog.coracle.social/posts/1687802006398
On the other hand, Nostr offers privacy by default. Let me copy-paste this from my recent blog:
The signing of events are done with the same public-key cryptography as you can find in bitcoin for signing transactions. Like Bitcoin, Nostr is not anonymous. Your identity is a pseudonym. You have full control of what you share with this pseudonym. If you desire full anonymity, you have to use clients which use the Tor network for example. Or use the Tor network on your behalf while using Nostr clients.