MySQL query r.e covering index with Primary Key
Short answer:  Yes.

Long answer:

You are using InnoDB, correct?  (Run SHOW CREATE TABLE j_data to find out what the Engine is.)

In InnoDB, each "secondary index" (contrast "primary key") silently contains a copy of the primary key.

So...  INDEX(j_name) happens to be identical to INDEX(j_name, j_id).

Tip:  At some point you will realize that prefixing all columns with the table name ("j_") is unnecessary clutter.