First communion, then communism?

No -- but perhaps a communionist? :-)

Actually, according to http://en.wikipedia.org/wiki/First_Communion , the term is first communicant.

The one who attends communion is known as communicant. source--http://dictionary.reference.com/browse/communicant?s=t

Since this is an English language stack exchange, I'll answer from the linguistic perspective.

Both have their etymological root in the same concept of bringing things together. Whether you are commuting to work (joining your workplace), a communist (joining a social community), or entering into a religious communion (joining with a church, and supposedly with its mythological deity).

The noun for someone who enters into religious communion is communicant.

The three sacraments of Initiation

• baptism
• confirmation
• communion

Of the three, Communion is the only one that is received repeatedly. The first communion is the initiation to the sacrament of Communion. And the child is the initiate to the sacrament.