I've always loved waterfalls and they were a favourite hiking destination back when I could walk with the dogs. There's something majestic about a huge waterfall, but even a small one is attractive to me because of the way the water is flowing and alive - not just standing still. That's what the Lord wants to be for us: an ever flowing fountain of life. David declared it in Psalm 36: 9 - With You is the fountain of life (māqôr hai).
A verse that was a favourite of mine, when I was a dancer in France back in the 1980s is the last verse of Psalm 87: Singers and dancers alike will say toutes mes sources sont en Toi - all my fountains, all my springs of joy are in You.
Isaiah echoed the same idea when he wrote: - With joy you will draw water from the wells/springs of salvation - mayan yeshua. (Is 12: 3)
Jesus Himself used this imagery, not only identifying Himself as the source of life, but also saying in John 7: 38 that rivers of living water would flow from those who believe in Him. Verse 39 explains that He was speaking about the Holy Spirit.
I remember that Jeremiah 2: 13 really stood out to me during one of my quiet times, also back in the 1980s. I wrote about it in my journal at the time. God says that His people had committed two evils: not only had they abandoned Him, the Fountain of Living Water - Māqôr Hai Mayim, they had also built cisterns for themselves - cracked cisterns that were incapable of holding water for long. It struck me that cistern water had probably been flowing at one time, but if kept in a cistern and not added to regularly, it would become stagnant... and a cracked, leaky cistern would eventually become empty. I felt challenged to keep receiving "fresh manna" from the Lord every day and not to depend on cistern water - old revelation from months or years previously.
So, this name of God reminds us that He is our Fountain of Living Water, and that He also wants that spring of life to flow within us, and then through us to others.