{% for m in entry.myMatrix if m.theName == nameImLookingFor %}
  {% if loop.index == 1 %}
    got the first one, it is {{m.theName}}
  {% endif %}
{% endfor %}

{% for m in entry.myMatrix if m.theName == nameImLookingFor %}
  got the first one, it is {{m.theName}}
  {% break %}
{% endfor %}