Upvote:5
The paper DS-11 form has only spaces for 21 characters for your last name, 17 for your first name, and 16 for your middle name. The online DS-11 form, which generates a file you must print, accepts 35 characters for each of first name, middle name and last name.
Unless you are this woman, that should be sufficient.
Your surname should not be truncated on the passport, but your middle or first names might be if they are too long. The names may also be truncated in the machine-readable data lines at the bottom of the information page. This doesn't affect your passport validity.