In Romeo and Juliet, how does Juliet "test" Romeo's love for her?

Juliet's primary "test" of Romeo's love for her is indeed
a difficult one.

Remember, everyone is masked; Juliet is
intrigued by Romeo, but she does not know who he is. She asks her nurse (who functions
somewhat like a nanny) to identify him.

The nurse tells
her,

His name
is Romeo, and a Montague,
The only son of your great
enemy.

Juliet is devastated.
She replies:

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My only love sprung from my only
hate!
Too early seen unknown, and known too late!
Prodigious birth
of love it is to me
That I must love a loathèd enemy
(1.5.136-41).

The Capulets
and the Montagues have a long history of animosity towards each other. Juliet and her
nurse know that there is absolutely no way her father will approve of his daughter being
in love with his mortal enemy. Moreover, Lord Capulet has already commanded that his
daughter marry the man of his choice, Paris.

With these
odds against her, Juliet knows that if she is to defy her family, she must be certain
that Romeo loves her. As she contemplates her situation, alone on her balcony, and
unaware that Romeo is hiding and listening, Juliet
pleads:

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Juliet:
O
Romeo, Romeo, wherefore art thou Romeo?
Deny thy father and refuse thy
name;
Or if thou wilt not, be but sworn my love
And I'll no longer
be a
Capulet.

Romeo:
[Aside]
Shall I hear more, or shall I speak at
this?

Juliet:
'Tis
but thy name that is my enemy:
Thou art thyself, though not a
Montague.
What's Montague? It is nor hand nor foot,
Nor arm nor
face, nor any other part
Belonging to a man. O be some other
name!
What's in a name? That which we call a rose
By any other word
would smell as sweet;
So Romeo would, were he not Romeo
call'd,
Retain that dear perfection which he owes
Without that
title. Romeo, doff thy name,
and for thy name, which is no part of
thee,
Take all myself
(2.2.33-39)

As you can see,
Juliet's "test" of Romeo is whether he will turn his back on his family. Like there
impetuous "relationship," this test is not well-thought out. What exactly would a pair
of elite teenagers do in the world? It's not like they have any particular skills. Romeo
passes the test, but the end result is tragedy.