Did we make up the word "limbo" or is it another name for hell so that it doesn't sound so bad?
There is a bit of confusion in the term and its meaning.
Here is some clarification. Limbo has never been considered a place of punishment like purgatory, or even less like hell.
The word and place called "limbo" have been developed as a hypothesis by theologians searching for a solution to the problem of innocent creatures that would not go to heaven because they were not baptized, nor to purgatory or hell because they died without sin. Limbo would be a place for example, for fetuses, embryos and babies who did not offend God and who died without being baptized.
The Church has never officially taught the existence of limbo, which would be a place of natural happiness.
If limbo does not exist, what happens to dead babies or to people who died without sin and without being baptized?
There could be other possibilities of salvation for those who have not been baptized through no fault of their own. God's mercy made Jesus come to save the world (Jn 12: 47). God's mercy can be exerted in different ways.
Baptism in water and in the Spirit is mandatory according to Christ's teaching: "Unless a man is born through water and the Spirit, he cannot enter the kingdom of God" (Jn 3: 5). Baptism makes us children of God and members of His Body, the Church.
The Church teaches that: "those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions, to do his will as they know it through the dictates of their conscience - those too may achieve eternal salvation" (Vatican II, Lumen Gentium, 16; The Catechism of the Catholic Church, 847).
"As regards children who have died without baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed the great mercy of God who desires that all men should be saved, and Jesus' tenderness toward children which caused him to say: 'Let the children come to me, do not hinder them', allow us to hope that there is a way of salvation for children who have died without baptism. All the more urgent is the Church's call not to prevent little children coming to Christ through the gift of holy baptism" (The Catechism of the Catholic Church, 1261).
Yes, God is good to children (Lk 18: 16), God who wishes all to be saved (I Tm 2: 4).