The Name of the Lord (Jehovah or Yahweh - the self-existent, eternal God) implies all the authority, honor, renown, character and atributes of God.
Strong tower - true fortress-type tower of great strength and security and majesty.
Psalm 9:9-10 The LORD also will be a refuge for the oppressed, a refuge in times of trouble. And they that know thy name will put their trust in thee: for thou, LORD, hast not forsaken them that seek thee.
Hebrews 13:5b-6 ...for He hath said, I will never leave thee, nor forsake thee. So that we may boldly say, The Lord is my helper, and I will not fear what man shall do unto me.
Psalm 20:7 Some trust in chariots, and some in horses: but we will remember the name of the LORD our God.
Daniel 11:32b... the people who know their God shall be strong, and carry out great exploit. NKJV
The people who know their God - know by seseing and as a familiar friend, to discern and discover and understand our Supreme, All-powerful, Creator God (Elohim).
Shall be strong and carry out great exploits - because we are fastened upon our God, we will be courageous, and God will strengthen, help, repair, fortify, and establish us as we war against and push down those spiritual forces of darkness and wickedness. (See Ephesians 6:10-20)
At the end of Proverbs 18:10 "strong" (NKJV) and "safe" (KJV) are both correct translations. Our Lord defends and protects us by setting us on high in Him, as in a strong, lofty, inaccessible tower.
The righteous run to it and are strong (KJV - safe) - just and lawful person runs, or actually, rushes to God.
Jonah - ran away from God
David - ran to God
Psalm 18:1-3 I will love thee, O LORD, my strength. The LORD is my rock, and my fortress, and my deliverer; my God, my stsrength, in whom I will trust; my buckler, and the horn of my salvation, and my high tower. I will call upon the LORD, who is worthy to be praised: so shall I be saved from mine enemies.
Joseph - ran to God
Genesis 50:19-20 And Joseph said unto them, Fear not: for am I in the place of God? But as for you, ye thought evil against me; but God meant it unto good, to bring to pass, as it is this day, to save much people alive.
Run to the Lord, Learn of Him, Worship, Seek to obey out of love!
Deuteronomy 33:27a The eternal God is thy refuge, and underneath are the everlasting arms...
He is a safe place for me to live, to abide.