Yes, yyyy-MM-dd is the ISO 8601 format for a date without time of day and without time zone.
To store into an SQL database using either a JDBC 4.2 or later driver or a modern JPA implementation such as Hibernate 5, you have got nothing to use a Date object for (no matter if you meant java.util.Date or java.sql.Date). I recommend that instead you use java.time, the modern Java date and time API. The class to use for a date without time of day is LocalDate. And you can store one into your database without any conversion.
LocalDate parses ISO 8601 format as its default, that is, without any explicit formatter:
    String receivedString = "1962-11-27";
    LocalDate dateOfBirth = LocalDate.parse(receivedString);
    System.out.println("Date of birth is " + dateOfBirth);
LocalDate also gives ISO 8601 format back when we print it:
Date of birth is 1962-11-27
I haven’t given you the full story yet, though. yyyy-MM-dd is the extended format that is by far most often used. There is also a basic format that is compacter in that it leaves out the hyphens: yyyyMMdd. I suggest that you insist on getting your date string in the extended format. If you cannot do that, you will have to specify a formatter for parsing:
    String receivedString = "19621127";
    LocalDate dateOfBirth = LocalDate.parse(
            receivedString, DateTimeFormatter.BASIC_ISO_DATE);
This will give you a LocalDate equal to and indistinguishable from the one we had before.
To save into your database using JDBC:
    PreparedStatement pStmt
            = yourDatabaseConnection.prepareStatement(
                    "insert into your_table (date_of_birth) values (?);");
    pStmt.setObject(1, dateOfBirth);
    int insertedRows = pStmt.executeUpdate();
Note the use of setObject(), not setDate().
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