pgp – Import secret key into GnuPg doesn’t work?

I would like to import a private key into GPG so I did:

gpg --allow-secret-key-import --import /path/to/key/key.asc
gpg: key 51D5DF493ECAFF88: "John Doe <>" not changed
gpg: key 51D5DF493ECAFF88: secret key imported
gpg: Total number processed: 1
gpg:              unchanged: 1
gpg:       secret keys read: 1
gpg:  secret keys unchanged: 1

But then, the key is not listed :

$ gpg --list-secret-keys | grep 51D5DF493ECAFF88

What’s wrong?

$ gpg --list-packets /path/to/key/key.asc | grep dummy

$ gpg --version
gpg (GnuPG) 2.2.4
libgcrypt 1.8.1