Is there any equivalent of the Shivoham experience in Christianity?

We can either be one with God, or not.

If not, then we can be on a path that takes us to God. If we are not on that path, we have our lifetime to straighten out and fly right, i.e Repent, but we never know when our time will come.

If we practice in all earnestness the 2nd part of the greatest commandment that Jesus gave us - Love our neighbour as ourselves - this is Agape love - then we are already with God, and we can say with assurance शिवोऽहम् (Shivoham), because we will be doing God's will, not our will, not the ego's will. But we cannot say it otherwise. In all humility it is not prideful to say I Am With God - शिवोऽहम् - if we are putting ourselves subservient to God's will, and doing it quietly without advertis*m*nt and looking for credit, enjoying the love we share, evidenced by our actions, to doubt it would be to doubt God. God is Love, and if we have Love, we are with God! This holds true for anybody of any faith or no faith, for religious, agnostics or atheists, Christians, Muslims, Hindus, Jehovah Witnesses, etc.

There is no Christian counterpart to Shivoham, since the concept of Cosmic Holistics, is considered to be Heretical.

In Christianity God is monotheistic, and yet tripartite; but equality to God is Heretical.

In Christianity God is supreme and all else is subservient to his will. And the idea that man can in any way alter the course of events through his own will is also Heresy.

In Christianity there are two realms the Spiritual realm and the material realm.

The material realm was created by God; who not only resides in the Spiritual realm, but encompasses the Spiritual realm which includes the Material realm, as a creation of an all powerful, all knowing, and ever present God. Therefore; to limit God's existence to part of his creation is illogical from the Christian concept.

As close as Christianity comes to Cosmic Holistics is:

John 17:11 (New King James version of the Bible) Now I am no longer in the world, but these are in the world, and I come to You. Holy Father, keep through Your name those whom You have given Me, that they may be one as We are.

That Christians become one as the trinity is one, does not remove them from their subservient role and as a matter of fact is affirmation of the being not only servants to God but also to each other as in:

Matthew 20:26 NKJV Yet it shall not be so among you; but whoever desires to become great among you, let him be your servant.

Matthew 23:11 NKJV But he who is greatest among you shall be your servant.

Mark 9:35 NKJV And He sat down, called the twelve, and said to them, "If anyone desires to be first, he shall be last of all and servant of all."

And so as you can see from these Scriptures, taken from the Holy Bible, which Christians consider to be God's instructions to his creation mankind. And deviation from his supremacy over his creation; which includes the Universe, is foreign to our basic beliefs.

In the terms you describe, most - if not all - forms of Christianity are Monotheistic in nature. That said, there are three key concepts (that again most forms of Christianity subscribe to) that are somewhat comparable to 'Shivoham' as you've described it: God's Immanence, the Indwelling of the Holy Spirit in a believer, the Glorification of believers.

Before describing those three concepts, I will firstly explain why Christianity* should be regarded as Monotheistic (versus Pantheistic) in character because God is transcendant over His creation:

...[this] means that God is above, other than, and distinct from all he has made - he transcends it all. - Theopedia.com

This is repeatedly implied in the Bible through descriptions of God as Holy (cf. Isaiah 6:3,Revelation 4:8,Leviticus 20:26) - ie separated, other, above - as well as stated more explicitly in certain passages such as:

8 “For my thoughts are not your thoughts, neither are your ways my ways,” declares the Lord. 9 “As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts. - Isaiah 55:8-9 NIV

The concept of the transendence of God in Christianity is antithetical to the concept of Shivoham.

Moving on to briefly outline the three more comparable concepts:

Firstly, The doctrine of the Immanence of God means:

..."to be within" or "near" in relation to God's creation. Immanence is closely related to God's omnipresence, in that God is always present within the universe, though distinct from it. God is 'within' the universe in that God is its sustaining cause. - Theopedia.com

This teaching empasizes the closeness of God to his creation and can be seen in passages such as:

27 God did this so that they would seek him and perhaps reach out for him and find him, though he is not far from any one of us. 28 ‘For in him we live and move and have our being.’ As some of your own poets have said, ‘We are his offspring.’ - Acts 17:27-28 NIV (emphasis added)

While this doctrine does not go to the extant of Shivoham in identifying God as inseparable from creation, it qualifies our understanding of transendence - God may be 'other', but He is not completely separated from His creation, rather He is close and His presence sustains it. This is an explicit disavowal of Deism.

Secondly, the doctrine of the Indwelling of the Holy Spirit in believers is inextricably linked to the concept of sanctification and teaches that not only is God 'close' in a particular way to them, but through the agency of the Holy Spirit, he allows them to become partakers in the divine nature:

Through these he has given us his very great and precious promises, so that through them you may participate in the divine nature, having escaped the corruption in the world caused by evil desires. - 2 Peter 1:4 NIV (emphasis added)

Most forms of Christianity are not universalist however, and this particular identification of the (renewed) nature of the believer with the nature of God is restricted to the 'household of faith'.

Finally, the doctrine(s) of the Glorification of the believer address the end stage of spiritual development and while appearing in somewhat different forms in the various branches of those who identify as Christian, most will affirm something very similar to:

...“glorification” is God's final removal of sin from the life of the saints (i.e., everyone who is saved) in the eternal state (Romans 8:18; 2 Corinthians 4:17). At Christ’s coming, the glory of God (Romans 5:2) – His honor, praise, majesty, and holiness-- will be realized in us; instead of being mortals burdened with sin nature, we will be changed into holy immortals with direct and unhindered access to God’s presence, and we will enjoy holy commune with Him throughout eternity. In considering glorification, we should focus on Christ, for He is every Christian’s “blessed hope”; also, we may consider final glorification as the culmination of sanctification.

Final glorification must await the manifestation of the glory of our great God and Savior Jesus Christ (Titus 2:13; 1 Timothy 6:14). Until He returns, we are burdened with sin, and our spiritual vision is distorted because of the curse. “For now we see in a mirror dimly, but then face to face. Now I know in part; then I shall know fully, even as I have been fully known” (1 Corinthians 13:12). Every day, we should be diligent by the Spirit to put to death what is earthly in us (Romans 8:13). - gotquestions.org

In conclusion, while there are some elements of the doctrines of Immanence, Indwelling of the Holy Spirit and Glorification that are somewhat comparable to the concept of Shivoham as described, they cannot be considered as identical, as they assume the transendance of God which explicitly denies it.

_{*Generally on this site, we seek to avoid characterising 'Christianity' as a whole, as there are many religions that claim such a label that possess exclusionary elements to each other. This is so even within the largest generally recognized meta grouping of Nicene Christianity (Catholics, Eastern Orthodox and Protestants). That said, 99.9% of Christian sects can be accurately characterised as monotheistic despite the very real distinctions in many other aspects of their theologies.}