What does Western Catholic infant baptism and confirmation involve, especially with regard to being identified as a Catholic?

My son’s grandmother was Roman Catholic and she wanted us to have him baptised without delay. However, given we did not intend to bring him up in the Catholic faith, that would not have been possible. I found lots of information in this article: [Infant Baptism](https://en.wikipedia.org/wiki/Infant_baptism#Roman_Catholic_Church) . I am also aware that confirmation takes place later, at around age 7, the age of discretion. Source: [Confirmation](https://en.wikipedia.org/wiki/Infant_baptism#Confirmation) Since then, I have wondered if baptised infants of Catholic parents are identified as being a member of the Catholic Church. Is a baptismal certificate given to the parents, and, if so, what does it say? Or does a child not become a recognised Catholic until after confirmation? And what obligations and responsibilities does that confer upon the child?