Not that long ago, some developers created a standard for saving wallet labels, where the data can be exported and imported among different wallets that support the standard.
My guess is that Electrum will add that sooner or later.
Do you mean BIP-0329?
Link:
github.com/bitcoin/bips/blob/master/bip-0329.mediawikiIf so, during the first few months, it seemed like it was going to be implemented quickly.
But for some reason, the one who is working on the implementation never updated his Pull Request for almost a year now.
The main developers aren't working on it either.
Link:
github.com/spesmilo/electrum/pull/8614