The roommate is right on this one. As Sternvogel’s above post says, and here’s another to reinforce it, (Scroll down for last sidebar), and another, too.
My limited French would have the original name pronounced with a soft T, silent H:
Teh-ruh, which makes sense in anglicising it to match “thorough”, or, easier, “furrow”. Someone with a better understanding of the French pronunciation could shed light on the transition of the name.
Like Zorro.
For me “thorough” is definitely “THUR-ow” with the “ur” as in “burp”.
My friend from Tennessee confuses me with her pronunciation of “oil”; she says it the way I say “awl” and “all”.
Also in Tennessee, I grew up calling kerosene coal oil. (Pronounced ko lawl.. I thought it was spelled c-o-l-o-i-l until I was grown.
Henry David Thur OH
THUR uh or even THUR in parts of North West Tennessee
Have you ever heard anyone pronounce Mrs. as if it were Miz Rez?
If you’re me, you say “He’s a good man, and thurah”, and you’re physically incapable of leaving off the first five syllables.
I’m with the OP.
Does “thorough” really have an “oh” sound on the end in US English? I’ve never heard it pronounced that way.
I say “THURR-uh” (with a schwa vowel on the end), to rhyme with “borough”.
Yep, and borough ends with an oh sound too. Hence the abbreviated form “boro”.
Unless you’re from Peterborough, Ontario. 
The problem, though, is that we’re talking about a personal name, and we don’t know how the actual Thoreau pronounced it. A word ending in -eau immediately sets off a trigger in our minds that the last syllable should be pronounced to rhyme with “roe” and, furthermore, that it should be accented. But according to the rules of French, if the word were going to be pronounced correctly, it wouldn’t be “tho-ROE”, but “to-ROE”.
Is there any record of how the man pronounced his name, or are there any living descendants who bear the name? How do they pronounce it?
On the other hand there is, or used to be, a dialect that seemed to be centered around Chicago, when final ‘o’ was replace with ‘a’. In the 1970s, the National Lampoon did a spoof of the Chicago Tribune which they titled The Chicaga Tribune. My grandmother who was from midstate Illinois pronounced things like that…Chicaga, tomorra, and so on. Don’t remember how she said ‘thorough’, but probably that followed the same pattern.
There’s a town in western New Mexico off I-40 named Thoreau. Everybody calls it thuh-ROO. I’d say his name was pronounced thuh-ROW, and thorough is pronounced THUR-o
Yes, it appears there are still pockets of America where people talk proper. 
The way folks around here pronounce Beaulieu as Bah-LOO. /shudder
This is the umpteenth thread at SDMB about pronunciation, and most of them have had the word “pronOunciation” in the title. Since this is the Straight Dope, I hope you don’t consider it rude of me to point out the misspelled word.
For what it’s worth, my native pronunciation is “thuh-ROW”, but when I was a kid and visited Walden Pond I was told by someone there that contrary to common pronunciation, he actually pronounced it just like the word “thorough”, with the stress on the first syllable.
Same here, and I would think that homonyms would have to have the accents in the same spots, thus being indistinguishable in sound.