I am constructing a survey for mothers to answer questions about their child/children. One of the first questions I want to ask is her child's name, then I wanted all of the questions that follow to put in said child's name, like a macro built within the survey, making it more personable than "child 1". Does Qualtrics have this feature?

You can use piped text to achieve this.

customizing a survey question with a name provided in the survey

customizing a survey question with a name provided in the survey | Experience Community