I can not register a person's name in my calendar

The error lies in how you structured the data in the structure. nome must be an array, not a vector. Doing:

typedef struct
{
  int numero[MAX];
  char nome[MAX][MAX];
  int tam;

} AGENDA;

In your code today, you are trying to save a string to a char, which is not possible. Since you want to use multiple strings, what you should do is use an array of characters.

One extra comment I would like to make is that, in particular, I would attack the problem differently. Instead of having the struct save all the contacts, have each struct store a contact and from there make a vector of Contacts. So the structure would become:

typedef struct {
  int numero;
  char nome[MAX];
} Contato;

I rewrote the code to show more or less how it is done. Note that there is still a lot of improvement in it. There are errors that can happen easily and are being checked, other details, but that's how you really do it, even something simple.

I created a new structure with the contact entry. If you want you can call it contact, but I do not know if it's suitable in a real context. In it will have the number and the name. The number I changed to string because it's usually the phone number, so struct is not appropriate . If it's something else, then it seems to make less sense to even let the person type this.

I have predefined that the name will have 30 characters, you can use the size you want.

I better control typing. You have flaws in using int so, but for an exercise that's fine.

I've given a better name to the function that initializes the calendar so that it's clear that you need to release it. And I created it before any way, even to avoid another mistake. And I changed the startup to reboot. There is an error there in the reboot, which I have in some way introduced, see if you can identify and fix it, so exercise really.

If you do not understand some point ask specific questions.

I made other simplifications and improvements. Since you want to learn pay attention to every detail, even in the spaces. I had others wrong that I corrected, it gets exercise to identify them.

#include <stdio.h>
#include <malloc.h>

#define MAX 50

typedef struct {
    char numero[12]; //permite um telefone nacional
    char nome[31]; //permite 30 caracteres
} Entrada;

typedef struct {
    int tamanho;
    Entrada *contatos;
} Agenda; 

void cadastrar(Agenda *agenda) {
    int op = 1;
    do {
        printf("Digite o telefone\n");
        scanf("%11s", agenda->contatos[agenda->tamanho].numero);
        printf("Digite o seu nome\n");
        scanf(" %30[^\n]", agenda->contatos[agenda->tamanho].nome);
        printf("Digite 1 para continuar 2 para parar\n");
        scanf("%d", &op);
        agenda->tamanho++;
    } while (op != 2);
}

void imprime(Agenda agenda) {
    for (int i = 0; i < agenda.tamanho; i++) printf("%11s - %s\n", agenda.contatos[i].numero, agenda.contatos[i].nome);
}

Agenda iniciaAlocaAgenda() {
    return (Agenda) { .tamanho = 0, .contatos = malloc(sizeof(Entrada) * MAX) };

}

void liberaAgenda(Agenda agenda) {
    free(agenda.contatos);
}


int main() {
    Agenda agenda = iniciaAlocaAgenda();
    int op = 1;
    do {
        printf("1-Adicionar numero\n");
        printf("2-Remover numero\n");
        printf("3-Procurar numero\n");
        printf("4-Imprimir\n");
        printf("6-Reincia a agenda\n");
        printf("7-Parar\n");
        scanf("%d", &op);
        switch (op) {
        case 1:
            cadastrar(&agenda);
            break;
        case 2:
        case 3:
            break;
        case 4:
            imprime(agenda);
            break;
        case 5:
            break;
        case 6:
            agenda = iniciaAlocaAgenda();
            break;
        }
    } while (op != 7);
    liberaAgenda(agenda);
}

See running on ideone . And no Coding Ground . Also I put it in GitHub for future reference .