Your Hungarian name means "smith" and is the second most common name in Hungary. It can be spelled Kovacs, Kovach, or Kovats, which are all the same name and variations can be totally ignored. There were certainly many Kovacs families in Upper Hungary, now Slovakia, and while you may have information that your family came from that region, it does not mean they were Slovak. Many Magyars did (and still do) live in Slovakia. On the other hand, there were Slovaks who took Magyar names, so you cannot be certain. Knowing what language they spoke would be important.
As for your "crest," which is properly the coat of arms, since the crest is only that portion that extends above the helmet, please refer to my response to Shandi Kovacs and my post on Kovacs families and coats of arms. In any case, your description does not sound very reliable. The vast majority of Hungarian coats of arms have blue shields, not red, and it is almost unheard of for a letter to appear on a coat of arms. I would be interested to learn where this description came from.