Hashamahyim = "הַשָּׁמַ֖יִם" = "The Heavens"
The ancient paleo-hebrew symbols reveal greater depth and interconnectivity of the Biblical text than is immediately apparent on the surface.

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"In the beginning, God created the heavens and the earth"
Genesis 1:1
Using the same principles I've used in the other Hebrew language studies on this site, below I look at the associated meanings of the hebrew letters in the word "Hashamahyim"
Hebrew Letter Meanings
Hey
Ancient
Modern
Image Association: Spirit, Man Raising Arms
Associated Nature: Look, Behold, Breath, Sigh, Revelation
Shin
Ancient
Modern
Image Association: Teeth
Associated Nature: God Initiated State Change, Destruction, Crushing, Pressing, Eating
This letter also has some association with a period of time. As in, over time something was changed/destroyed/crushed rather than an instantaneous event.
Mem
Ancient
Modern
Image Association: Water
Associated Nature: Chaotic, change, transformation, ever-changing, people, nations, languages, tongues, knowledge
The association of water is where the other meaning associations come from. Man is predominantly water in chemistry and therefore the nations too are made up of predominantly water. Knowledge in its many forms is produced from a thirst for understanding by which the waters of God's knowledge & wisdom satisfy. We find this is directly applicable to statements in the ministry of Jesus in which He self-describes as both "The Word" and "the source of living water" indicating that He is the source of life-giving truth — the Gospel.
Also noteworthy, Mem has two forms - an open and a closed which represent revealed truth & heavenly mysteries
Yud
Ancient
Modern
Image Association: Hand, Arm
Associated Nature: Hand, Work, Throw, Worship
This letter also has some association with an instance in time, particularly a beginning. As in God bringing something into existence with his hand.
Hashamayim - The Waters Divided
"And God said, 'Let there be a vault between the waters to separate water from water.' So God made the vault and separated the water under the vault from the water above it. And it was so. God called the vault “sky.” And there was evening, and there was morning—the second day."
Genesis 1:6-8
Using the associated meanings for each of the letters above, we can see that the combined meaning translates to an identical description of how it was made in the Genesis verse above. Behold (He) God initiated change (Shin) His hand (yud) divides water (Mem) and water (Mem). Literally, in the word we see the representation of God's hand between two Mem's representing the waters above and the waters below.