Synonyms for Reel off:

n.

register, catalog, index, sign up, sign in, tabulate, waitlist, reference. rattle off (noun)
specify, recite, enumerate, list.
reel off (noun)
unreel, roll off, spiel off, rattle down, rattle off.

v.

contact (verb)
unreel.
rattle (verb)
list.
recite (verb)
enumerate.
tell (verb)
recite.

Other synonyms:

recite. Other relevant words:
list, recite, enumerate.