If that's your actual data object, then data[0].name would give you "Maria". If I'm reading this right, though, you want to get all the names from the project array. You can use Array.map to do it fairly easily. Note the use of an ES6 arrow function to quickly and easily take in the object and return its name.
var bigObject = [{"id":1,"name":"Maria","project":[{"id":5,"name":"Animals"},{"id":6,"name":"Cats"}]}];
var smallObject = [{"id":5,"name":"Animals"},{"id":6,"name":"Cats"}];
console.log("Getting the names from the full array/data structure: "+bigObject[0].project.map(obj => obj.name))
console.log("Getting the names from just the project array: "+smallObject.map(obj => obj.name))
EDIT: As per your comment on the other answer, you said you needed to use the solution in this function:
"render": function (data, type, row) {if(Array.isArray(data)){return data.name;}}
To achieve this, it looks like you should use my bottom solution of the first snippet like so:
var data = [{"id":5,"name":"Animals"},{"id":6,"name":"Cats"}];
function render(data, type, row){
if(Array.isArray(data)){
return data.map(obj => obj.name);
}
};
console.log("Render returns \""+render(data)+"\" as an array.");