Intention is an extremely crucial and integral aspect of worship in Islam. This is true of Prayer, fasting, zakah and Hajj. It also applies to all of the acts of devotion and good works that we perform.
Regarding your question, it should be clear that making one’s intention is an essential component of Prayer. One should have the intention in the heart to perform such-and-such a Prayer.
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states: Niyyah is considered an essential condition or integral part of each and every act of worship such as salah, zakah, fasting, and Hajj. Just as niyyahfard (obligatory) Prayers, it is also required for the validity of sunnah and nafl Prayers as well. Imam Fudhayl ibn `Iyad said, “All acts of worship in order to be valid must fulfill two conditions: They must be sanctioned by the Shari`ah; secondly, they must be done with the sincere intention of pleasing Allah.”

Aside from cherishing the intention of performing an act of worship for the sake of Allah, one must also formulate in one’s mind the intention to perform the specific Prayer intended. Thus, just as it is important to make the intention of praying `Isha’ prior to doing it, likewise, one should have the intention of praying Witr or Tahajjud, and so on, respectively prior to performing the same. In other words, the niyyah for each Prayer should be done while one is ready to pray the same. Thus there is no need to formulate the niyyah of Witr while praying `Isha’. In the case of Tahajjud the niyyah of Witr should be done in the last odd number of rak`ahs one is performing.
Uttering words of intention, however, is not considered a requirement; it is simply a custom that has been developed in later generations. Some scholars consider it to be a bid`ah (innovation) to be avoided, while others tolerate it under the pretext that it facilitates formulating the niyyah. But as Imam Ibn Al-Qayyim has said, since niyyah is an action of the heart or mind, mere utterance of words without cherishing the intention in the heart or mind would not be deemed as sufficient.