Do I have to give Notice to Designate Non-Expert trial witnesses?

If you have not been served any discovery, you still should check the both the local rules and the Court's rules to see when you have to exchange witness lists and exhibits.

Generally speaking, in Texas state court you are not required to disclose the identity of your potential fact witnesses prior to exchanging witness lists unless specifically requested to do so by way of Request for Disclosure or Interrogatory. However, if you haven't been served with a Request for Disclosure, I'm assuming you haven't propounded one on the other side either (otherwise, they would have remembered to do so upon receiving yours). You will have to weigh whether it's strategically to your advantage that neither side knows the identity of the other's potential fact witnesses prior to the exchange of witness lists.

I can't speak for the rules of procedure in Texas, but I'll generally say that I'm not giving a party free discovery or any additional information beyond the information an opposing party specifically requests in discovery. It's not my job to try the other side's case. So, so long as you're in compliance with what you're supposed to do under the rules, and so long as the other side hasn't requested in discovery a list of potential witnesses to the case, then your only obligation would be to disclose those in your witness list if that's required to be exchanged at a Pretrial Conference. Check your rules to ensure that you're not required to make any disclosures before that time.