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"...that they may be one, even as we are one." Are "they" to retain an individual identity or are "they" to become God in the same manner you say Jesus is God?

The Father, Son, and Holy Spirit have always had their individual personhood (identity) and that will never change. Therefore, the Father and Son will not "become" God, as they are both already God. They are simultaneously both God and individual Persons within the Trinity.

Jesus did not ever claim to be God. Rather, He said "I am in the Father and the Father is in me,..." and this is the same he asks for you.

Yes, Jesus did claim to be God. Here is an example:

John 8:48-59 : 48 The Jews answered him, “Aren’t we right in saying that you are a Samaritan and demon-possessed?” 49 “I am not possessed by a demon,” said Jesus, “but I honor my Father and you dishonor me. 50 I am not seeking glory for myself; but there is one who seeks it, and he is the judge. 51 I tell you the truth, if anyone keeps my word, he will never see death.” 52 At this the Jews exclaimed, “Now we know that you are demon-possessed! Abraham died and so did the prophets, yet you say that if anyone keeps your word, he will never taste death. 53 Are you greater than our father Abraham? He died, and so did the prophets. Who do you think you are?” 54 Jesus replied, “If I glorify myself, my glory means nothing. My Father, whom you claim as your God, is the one who glorifies me. 55 Though you do not know him, I know him. If I said I did not, I would be a liar like you, but I do know him and keep his word. 56 Your father Abraham rejoiced at the thought of seeing my day; he saw it and was glad.” 57 “You are not yet fifty years old,” the Jews said to him, “and you have seen Abraham!” 58 “I tell you the truth,” Jesus answered, “before Abraham was born, I am!” 59 At this, they picked up stones to stone him, but Jesus hid himself, slipping away from the temple grounds.

The Jews tried to stone Him because they knew EXACTLY what Jesus was claiming. They knew their scriptures, including:

Ex. 3:13-14 : 13 Moses said to God, “Suppose I go to the Israelites and say to them, ‘The God of your fathers has sent me to you,’ and they ask me, ‘What is his name?’ Then what shall I tell them?” 14 God said to Moses, “I AM WHO I AM. This is what you are to say to the Israelites: ‘I AM has sent me to you.’ ”

What other reason could they have possibly had for immediately wanting to stone Him than for claiming to BE God?

"“I tell you the truth,” Jesus answered, “before Abraham was born, I am!” 59 At this, they picked up stones to stone him, but Jesus hid himself, slipping away from the temple grounds.
The Jews tried to stone Him because they knew EXACTLY what Jesus was claiming. They knew their scriptures, including:

Ex. 3:13-14 : 13 Moses said to God, “Suppose I go to the Israelites and say to them, ‘The God of your fathers has sent me to you,’ and they ask me, ‘What is his name?’ Then what shall I tell them?” 14 God said to Moses, “I AM WHO I AM. This is what you are to say to the Israelites: ‘I AM has sent me to you.’ ” What other reason could they have possibly had for immediately wanting to stone Him than for claiming to BE God?"

Very Good, FK!

"But wherefore said He not, "Before Abraham was, I was," instead of "I Am"? As the Father uses this expression, "I Am," so also does Christ; for it signifies continuous Being, irrespective of all time. On which account the expression seemed to them to be blasphemous. Now if they could not bear the comparison with Abraham, although this was but a trifling one, had He continually made Himself equal to the Father, would they ever have ceased casting stones at Him?" +John Chrysostom Homily 55 on the Gospel of John