Not sure why you mentioned "registration details" and not a signed message, just in case you think Electrum is like some sort of Coinbase/Blockchain.com, they're not. A non-custodial wallet is not like a company that maintains a database of registered users.
this ^^ is correct, i'm just trying to rephrase what joniboini said in a newbie-friendly way. It's slightly simplified, but i hope i'll do a good job at an ILI5 explanation:
Bitcoin is completely decentral. All you need to spend bitcoin is a private key. A public key gets derived from this private key, the public key gets hashed, and the result of this hash is your address.... This address can get funded by unspent outputs (you get payed). So, if you have a private key, that's enough.
Now, one step further: nobody needs to know you have this private key... You can create millions of private keys (and derive addresses from them) on your offline pc... All of them will be valid (well, if you didn't mess up the creation process)... If you'd copy an address from this offline machine and give it to somebody else to get payed, the only thing that will be known to anybody else (but you) is said address.
You don't need to register anything, you don't need to share anything (except for the address in case you want to be payed).
Offcourse, there are online company's that manage those private keys for you... These online company's can have rules (for example, registration or KYC). I'd strongly advise against using said company's, because they controll all your funds (they're the one knowing your private keys, so they take all controll away from you).
Instead, i'd advise you to use a decent desktop, hardware, paper or offline wallet... These wallets do a pretty good job at managing your keys, taking away most of the technical details so you don't have to worry about them... But even then, once again: nobody needs to know you own any bitcoins, there is no central authority, no need to register...
