“In this manner, therefore, pray: Our Father in heaven, Hallowed be Your name.”
Question: What does this mean, how have you experienced that?

Thy name

I learned a long time ago that the use of the word “name” in the bible can be taken to mean not just the words listed in the name, but the person himself as indicated by the name.

Hallowed

The word “Hallowed” or “made holy”, reminds me of two fundamental commands in the bible:
To the people of Israel in Leviticus 19:2, “You shall be holy, for I the Lord your God am holy”
And from Jesus as he amplified what this meant in Matthew 5:48, “Therefore you shall be perfect, just as your Father in heaven is perfect”
So it points to the many aspects of God, which are completely different to, or set apart from, the sinful nature of this fallen world; of how God is perfect in goodness, perfectly righteous, and perfect in truth and wisdom.

Our sinful state

This points to the gulf between who we are as sinful human beings, and who we were meant to be as made in the image of God, and of who we need to be in order to be acceptable to Him.
That gulf has been bridged for us by Jesus on the cross, for only a miracle could make us acceptable to God and therefore to one another. But in a sense that bridge is one way; even while Jesus came to live amongst us, He remained perfectly sinless in every way. And we cannot hold onto our sin if we are to be carried across that gulf.

This prayer is a reminder that while Jesus, although God, came to live amongst us and save us, and gave us access to our heavenly Father, that close familiarity with his presence should never allow us to be casual about our sin, or presume it is acceptable to God. The new heart He gives us, and the new self that his Holy Spirit is creating in us, are acceptable both to God and to our true selves, while our old selves are unacceptable in every way.

It also reminds me of the problem of the evangelism style which tells people that Jesus is their greatest mate and leaves it at that. He is, but we only understand why when we see how much we don’t deserve His self-sacrificing love.
Even while we know we are fully loved more deeply than we can imagine, we are not loved because of our sinful state, but despite our sin. And we need to see ourselves in the same way, as precious to God and therefore to one another, but fully repentant of our continual failings before God.

May I always recognise the person and presence of God in my life as being all that is perfectly good and righteous, and how that is the complete opposite of my “natural” state and the natural state of our world.