Tranquility seems a bit too much a typical English word, i.e. not that accessible or directly associative to people with another native language, even when they already know the meaning.
And speaking for myself, I also think it’s a bit too far from the browsing action and (thus) tasting a bit too much of marketing.
There are countless examples of software with names that do not associate with the function of the software. Just in the browser market alone we have Opera, Firefox, Epiphany and Chrome (though the latter is sort of a browser developer inside joke.) Fairly quickly people learn what these names mean and associate them with the software, and tend to forget the original meaning.
Names always have an element of marketing in them. I hope this software makes browsing the web a smooth, fast and fun process and just stays out of the user’s way, and I think the name reflects that.
Indeed, Tranquility kind of follows the path Linux folks took by choosing the name Epiphany.
I can assure you that from the mentioned examples of Epiphany, Opera, Firefox and Chrome, Epiphany is the weakest for non-native speakers (I’m one of them).
The other names still offer a comprehensible, strong, pleasant and broad enough ‘palette’ of other associations to this group of people.
For example Chrome is good, everybody loves shiny things, chrome keeps out rust, signifies newness and so on.
Opera visually is the impressive highpoint in a solo brought with much skill, emotion, tonal perfection and theatre filling volume.
With Firefox it’s even easier: probably anything with ‘fire’ in it is ferocious and the whole world knows the fox as a shrewd animal.
And Epiphany? I’m not ashamed to admit I even had to look up its meaning.
The more universal word for tranquil could be ‘peace’, consider what an instant ring that word has around the world! (Mind you, I’m not saying ‘Peace’ would be a good name for a browser here…)
What I also don’t like is the reinforcement Tranquility has of the Japanese/Eastern/Zen cliché visual image of ‘the old monk meditating alone in his remote ancient temple surrounded by mountains shredded in morning fog’ etc…
When you look at Haiku’s themselves, they can be funny, disquieting, deeply human, honest, sad, joyful and a lot more…
What tranquility does have to do with Haiku’s is that Haiku’s probably are born in a tranquil environment…but that’s a secondary association to their actual content and character.
This secondary aspect of it leads to the marketing (in the bad, superficial sense of the word) taste of the name.
As a last remark: you talked about ‘a smooth, fast and fun process’. I don’t want to be word-picking but tranquil and fast aren’t related per se, they can easily be each other’s opposite as well.
Is again “Haiku”: Hyper Access to Information / Internet (and) Knowledge Unit. Though even I myself feel a “Unit” falls short of an apt reference.
And on occasions where differentiation has to be made between the OS and browser, call it HB, the Haiku browser.
how about Aria Browser?
http://en.wikipedia.org/wiki/Aria
easy to pronouce “Ah-ree-ah” descriptive hopefully of the browser we could expect on Haiku.
I can’t find any reason not to use the name it isn’t an obvious name like net-whatever web-etc which sound a bit 90’s i guess heh…
oh there appears to he an API something to do with javascript called ARIA but I don’t thing that would be of any concern to users http://wiki.codetalks.org/wiki/index.php/Web_2.0_Accessibility_with_WAI-ARIA_FAQ#What_is_ARIA_and_how_does_it_enable_accessible_JavaScript_widgets_today.3F
On Be, “Stinger” first came to my mind. With a cup of Java I can further relaxed for inspiration: Is it a pleasure to taste a haiku with MEAD, the Haiku honey wine?
I, as a Japanese, am afraid of the confusion of naming as well. “Haiku” is unique for sure but it should be the only word from Japanese in my opinion.
So my two cents is … “Loom: Weave the Web”. I know I’m bad at English. 
As everyone is insisting on Japanese words here what about.
Nakama - meaning colleague, comrade…
and for a login manager we could have the word “konichiwa” or an rss reader or daily comics reader called “ohayo” or a nightly backup tool called “kombanwa”
Is everything going to have Japanese names?
I suggest the Japanese word “ensoku” meaning “excursion” (similar to Kiswahili “safari”).
+1 for Aria
I think Aria is actually a really great name. In general, I think that Haiku should use names from words/terms of artistic expression. If everything is a variation of Haiku, poem, or something japanese, we’d dilute the meaning and emotion of “Haiku”. Further, this relatively open theme leaves room for creativity, while still creating an ecosystem for the brand.
+10 for Aria
Then again, to not follow my proposed them, I like:
Boulevard
Lantern
Pyramid
I like to think about the name holistically: Imagine it rendered into an icon, the page you see when you first run it, the whole thing.
How about
Just random suggestions :)!!
Regards
Amol
If you want something about “journeys” then pick the word “densetsu”!! 
Haiku browser might be Webkit-based. Add some Haiku-related notion to it, like H…
WebHit or
webHit
It’s a bit buzzwordy, self-containing and easy to say out loud - only two syllables.
It can also be abbreviated in a nice way - webH (a bit like Net+).
I like H+ or Kimono.
tranquility? serenity? pyramid? what? It should have something to do with browsing. Surfer, netSomething, webSomething, wanderer, marauder… just brainstorming. But definitely not something as abstract and unrelated as ‘tranquility’.
Then why we don’t just settle on ‘Boredom’.
I think we should keep out all usual or easy words for this kind of app (web, net, browser…)
It should be a short word, fresh and related with the sense of the OS if possible…
I like:
Zen
Kigo
Haiga (but is related better with images)
Renga
But of the easy names, I like:
Surfing or surfer
I think WebSaylor would be a nice name for the native web browser in Haiku…
How about Bikeshed?
That may just have been the best suggestion I’ve heard so far 
I think Tranquility is just about perfect. Wasn’t it associated with the space program? (Other than the Sea of Tranquility.) That also suggests exploration, modern modes of transportation, scientific advancement, and (often serendipitous) discovery. Japanese culture values tranquility. Haiku is written to describe an instant in time, often a perfect moment, always evocative.
And here I was trying to work out something with Noh (traditional theatre). Add my vote for Tranquility.