Because he's small and runty.
The following quote from the animated series Dragons: Riders of Berk is the most canonical proof I've found:
Hiccup: I mean, think about it. Even my name! You know, it's Viking tradition to call the runt of the litter a hiccup.
(Random guy in the background calling a sheep): Come on, little hiccup.
(It turns out to be rather tiny)
(The same guy, towards Hiccup): Oh! Hey, Hiccup.
-- From the episode The Portrait of Hiccup as a Buff Man.
The Wikia here also backs this up:
Hiccup seems to have gotten his name from the fact that he was born early, so he was smaller and weaker than the other babies.
Re the quote you give: yes, it could suggest that he got the name because people thought it was "hideous", but I agree with @beichst's interpretation: he means that other kids get hideous names because their parents believe it will frighten off gnomes and trolls, but his parents didn't bother because he wasn't very fearsome anyway.
Out of canon, you may also be interested in this rather badly written fanfic entitled "The Reason for his Name", which gives another possible reason.