How to delete a record from a file in C?

I'm doing a practice with binary files in C, it's a Contacts directory in which you can save, show and delete contacts. I have made the functions but at the time of deleting a contact what I do is ask the user to enter the name of the contact to be deleted and read the file where the contacts are stored and while doing that I am writing an auxiliary file contacts minus the one have the name entered, after this I overwrite the original file by the auxiliary. My problem is that in doing this I delete all the contacts instead of just the one that enters.

        //Agenda
        #include <stdio.h>
        #include <stdlib.h>
        #include <conio.h>
        #include <string.h>
        #define NAME_ARCHIVE "contacts.bin"
        #define NAME_ARCHIVE_AUX "contacts_aux.bin"
        //Contactos
        typedef struct contacts{
            char name[20];
            char direcction[30];
            int phone;
        }Contacts;
        //Funciones
        void menu(char *nameArchive);
        Contacts createContact();
        void saveContact(Contacts contact, char *nameArchive);
        void showContacts(char *nameArchive);
        void deleteContact(char *nameArchive);
        void stop();

        int main (){

            menu(NAME_ARCHIVE);
            stop();
            return 0;
        }

        void menu(char *nameArchive)
        {
            int op;
            do{
                system("cls");
                printf("[1]Create contact\n");
                printf("[2]Show contacts\n");
                printf("[3]Delete contact\n");
                printf("[4]Exit\n");
                printf("Login option: ");
                scanf("%i",&op);
            if(op>0 && op<5){
                system("cls");
                switch(op){
                    case 1:
                        saveContact(createContact(),NAME_ARCHIVE);
                        break;
                    case 2:
                        showContacts(NAME_ARCHIVE);
                        break;
                    case 3:
                        deleteContact(NAME_ARCHIVE);
                        break;
                    case 4:
                        exit(1);
                    default:
                        printf("wrong choice\n");
                        stop();
                }
            }
            }while(op!=4);
        }
        //Creando el contacto
        Contacts createContact()
        {
            Contacts contact;
            printf("Name:\n");
            fflush(stdin);
            gets(contact.name);
            printf("Direcction:\n");
            fflush(stdin);
            gets(contact.direcction);
            printf("Phone number:\n");
            scanf("%i",&contact.phone);

            return contact;
        }

        void saveContact(Contacts contact, char* nameArchive)
        {
            FILE* file;
            //si el archivo existe va a
            //gregar el nuevo contacto que creamos al final del archivo
            //no va a sobreescribir
            file=fopen(nameArchive,"ab");

            if(!file){
                printf("Error\n");
                stop();
            }
            else{
                //Recibe 4 parametros:
                //1-Dirección de memoria de la variable que queremos guardar
                //2-El tamaño del tipo de dato
                //3-La cantidad de datos que queremos guardar
                //4-La variable del archivo
                fwrite(&contact, sizeof(Contacts),1, file);
                printf("Contact Save!\n");
                stop();
                fclose(file);
            }

        }

        void deleteContact(char *nameArchive)
        {
            system("cls");
            FILE *file, *fileAux;
            Contacts contact;
            fileAux=fopen(NAME_ARCHIVE_AUX,"wb");
            file=fopen(nameArchive,"rb");

            if(!file){
                printf("Empty\n");
            }
            else{

                char name[20];
                printf("Name of the contact to delete:\n");
                fflush(stdin);
                gets(name);
                //Recibe los mismo parametros que fwrite
                while(fread(&contact, sizeof(Contacts),1, file)){

                    if (!strcmp(contact.name,name))
                    fwrite(&contact, sizeof(Contacts),1, fileAux);
                }
                fileAux=fopen(NAME_ARCHIVE_AUX,"rb");
                file=fopen(nameArchive,"wb");
                while(fread(&contact, sizeof(Contacts),1, fileAux)){

                    fwrite(&contact, sizeof(Contacts),1, file);
                }

            }

            stop();
            fclose(file);
            fclose(fileAux);
            remove(fileAux);
        }
        //Mostrar contactos
        void showContacts(char *nameArchive)
        {
            FILE *file;
            file=fopen(nameArchive,"rb");
            if(!file){
                printf("Empty\n");
                stop();
            }
            else{
                Contacts contact;
                printf("%-20s %-30s %-30s\n", "Name", "Direcction","Phone");
                //recibe los mismo parametros que fwrite
                while(fread(&contact, sizeof(Contacts),1, file)){
                    printf("%-20s %-30s %-30i\n", contact.name, contact.direcction,contact.phone);
                }
                fclose(file);
                printf("\n");
                stop();

            }
        }

        void stop()
        {
            printf("Press any key to continue...\n");
            getch();
        }