What does Western Catholic infant baptism and confirmation involve, especially with regard to being identified as a Catholic?
Children baptized as infants are recognized as being Catholics, regardless if the parent really bring the child up in the Catholic Faith or not. All children who die and are baptized in the Church may be buried in the Church. Even after the age of reason they will be recognized as Catholics, but are not allowed to receive other sacraments until the sacrament of confirmation and reconciliation have been received. Until then they are often seen as Catholics who are not practicing their faith.
The child must be properly educated in order to be confirmed in the Latin Rite. If he or she does not attend religious formation classes, they will not be confirmed or receive communion in the Church until properly instructed. Some such Catholics eventually attend RCIA (Rite of Christian Initiation of Adults) as adults in order to become fully incorporated into the mystical body of Christ.
Eastern Rite Catholics are confirmed at baptism.
I know some priests that will baptize the first child of parents that are of dubious in their possible commitments and will refuse baptism for a second child if the first is not instructed in the faith. Other priests will baptize a second and third child in the hope that parents will eventually educate the children as Catholics.
At the baptism of a child in the Catholic Church, the parents will receive a baptismal certificate.
The parish registry will contain the listing in addition of the child’s name, the parents names, the godparent’s names, the priest who performed the baptism and the name of the parish church where it was performed.
The place of baptism is very impossible for a practicing Catholic to remember. Each additional sacrament such as confirmation, marriage, ordination to the priesthood will be sent to person’s church of baptism and the information will be inscribed into the official baptismal registry of the individual. Catholics may request this information at any time. It is obligatory for entering a seminary or a Religious Order.
Here is an example for such a request from the Archdiocese of Toronto, Canada.