Use Web3's getChainId() to get the chain ID.
Then map the returned chain ID into the list of known networks from https://chainid.network/chains.json, where the currency symbol is in the nativeCurrency nested object.
this is maybe too simple - but in my case, restarting my react app and my local blockchain solved this problem.
Also I recognized that I run into that issue a lot while using Firefox. It also helped me to switch the browser to Google Chrome.
The Renaissance and I got to the conclusion, that switching to any Chromium browser (eg Chrome, Chromium, Brave, and I ...