Avoid using strcat().  Instead, use strncat() or strlcat() ...
... Note that strncat() can also be problematic.

#include <stdio.h>
#include <string.h>
/* Compile: cc -g -ansi -pedantic -Wall -O2 -o concat-strings concat-strings.c */
/* Run: ./concat-strings */

#define MAX_LEN_FULL_NAME 20
#define ERR_MSG "Error: the string '%s%s' would be too long to fit into the variable of %d chars (terminating NULL included)."

int
main(int argc, char *argv[])
{
  char full_name[MAX_LEN_FULL_NAME];

  /* Command line argument check. */
  if (argc != 3)
  {
      printf("Usage: %s <first_name> <last_name>\n", argv[0]);
      return 1;
  }
  /* Check strings before copy. */
  /* Length of first name can be at most MAX_LEN_FULL_NAME - 1 (don't forget the NULL char!). */
  if (strlen(argv[1]) > MAX_LEN_FULL_NAME - 1)
  {
      fprintf(stderr, ERR_MSG, "", argv[1], MAX_LEN_FULL_NAME);
      return 1;
  }
  /* Copy first name to full_name. */
  (void)strncpy(full_name, argv[1], MAX_LEN_FULL_NAME - 1);

  /* Check strings before concatenate. */
  /* Length of first name plus length of " " can be at most MAX_LEN_FULL_NAME - 1. */
  if (strlen(full_name) + strlen(" ") > MAX_LEN_FULL_NAME - 1)
  {
      fprintf(stderr, ERR_MSG, argv[1], " ", MAX_LEN_FULL_NAME);
      return 1;
  }
  /* Concat first name and space. */
  (void)strncat(full_name, " ", MAX_LEN_FULL_NAME - strlen(full_name) - 1);

  /* Check strings before concatenate. */
  /* Length of first name plus length of " " plus length of last name can be at most MAX_LEN_FULL_NAME - 1. */
  if (strlen(full_name) + strlen(argv[2]) > MAX_LEN_FULL_NAME - 1)
  {
      fprintf(stderr, ERR_MSG, full_name, argv[2], MAX_LEN_FULL_NAME);
      return 1;
  }
  /* Concat last name to first name, separated by a space. */
  (void)strncat(full_name, argv[2], MAX_LEN_FULL_NAME - strlen(full_name) - 1);

  /* NULL-terminate string. */
  full_name[MAX_LEN_FULL_NAME - 1] = '\0';

  printf("Your name is '%s'.\n", full_name);
  return 0;
}

#include <stdio.h>
#include <string.h>
/* Compile: cc -g -ansi -pedantic -Wall -O2 -o concat-strings concat-strings.c */
/* Run: ./concat-strings */

#define MAX_LEN_FULL_NAME 20

/* Protoype */
void errmsg(int);

int
main(int argc, char *argv[])
{
    char full_name[MAX_LEN_FULL_NAME];
    if (argc != 3)
    {
        printf("Usage: %s <first_name> <last_name>\n", argv[0]);
        return 1;
    }
    /* Copy first name to full_name. */
    if (strlcpy(full_name, argv[1], sizeof(full_name)) >= sizeof(full_name))
    {
        /* Error: destination string 'full_name' was truncated. */
        errmsg(MAX_LEN_FULL_NAME);
        return 1;
    }
    /* Concat a space char to first name. */
    if (strlcat(full_name, " ", sizeof(full_name)) >= sizeof(full_name))
    {
        /* Error: destination string 'full_name' was truncated. */
        errmsg(MAX_LEN_FULL_NAME);
        return 1;
    }
    /* Concat last name to first name, separated by a space. */
    if (strlcat(full_name, argv[2], sizeof(full_name)) >= sizeof(full_name))
    {
        /* Error: destination string 'full_name' was truncated. */
        errmsg(MAX_LEN_FULL_NAME);
        return 1;
    }
    printf("Your name is '%s'.\n", full_name);
    return 0;
}

void
errmsg(int maxlen)
{
    /* Error: destination string was truncated. */
    printf("Sorry, this program only accepts full names shorter than %i characters\n \
            (including 1 space character as a separator).\n", maxlen);
}