The Shulhan Aruch (O.H. 110:4) says that when one embarks on a journey, one should recite a special prayer, known as Tefilat Haderech. Although Tefilat Haderech ends off with a blessing, the Shulhan Aruch does not discuss it in the laws of blessings but rather in the laws of prayer. The practical implication of this is that, according to Rabbi Shlomo Zalman Auerbach (Ishe Israel, ch. 50, note 4), since it is a prayer, one could insert a personal request. For example, one could request to be protected from a car accident while taking a road trip. On the other hand, Rabbi Haim Kanievsky says that the prayer already includes a reference to “all types of calamities” and this would therefore include car accidents and the like.
The Shulhan Aruch (ibid:7) says that Tefilat Haderech should only be recited if one’s journey is at least a Parsa in length (roughly 4 km or 2.5mi) beyond the city limits. Rabbi Ben Zion Abba Shaul (Or Lezion, vol. II) and Rabbi Shlomo Zalman Auerbach (Halichot Shlomo, ch. 21, § 3) both add that as long as one is driving among a constant stream of cars, one is considered to still be within the city limits and one should not recite Tefilat Haderech.
Regarding whether or not to recite the blessing of Tefilat Haderech with Hashem’s Name (also referred to as Shem Umalchut) in general, there is a well established Moroccan custom not to do so. The commonly used Siddurim Tefilat HaHodesh, Bet Oved and Patah Eliayhu all have Tefilat Haderech without Shem Umalchut. The Pri Hadash says that since the Rambam did not discuss Tefilat Haderech at all, then if one wishes to recite it, it should be done without Shem Umalchut. This approach is supported by Rabbi Ovadia Hedaya (Yaskil Avdi, vol. VII, Kuntres Achran, §3), Rabbi Shem Tov Gagin (Keter Shem Tov, pg. 634) and Rabbi Matzliah Mazuz (cited in Magen Avot, Orah Haim, § 110), who all say this is the Sephardic custom.
It should be noted that some Moroccan Poskim, such as Rabbi Yehoshua Maman (Emek Yehoshua, vol. I, Orah Haim, § 40) and Rabbi Shlmo Amar (Shema Shlomo, vol. III § 5), write that the blessing at the end of Tefilat Haderech should be recited with Shem Umalchut. Even for those who follow this opinion, it would only apply to a road trip that is beyond the city limits and is in a desolate area, or on a flight.
Summary: The common custom is to recite Tefilat Haderech without Hashem’s Name. If one has a custom to recite it with Hashem’s Name it should only be in situations with truly warrant the recital of Tefilat Haderech.