I received a junk fax about mortgage rates, asking me to call
800-611-8612 or 877-400-0758 (just one example, I have others). No
company name or sending fax number was listed.
How can I find out what company is behind these numbers?

all i can tell you is that 800 numbers (any 8xx number) is stored in a
database called SMS/800 which is maintained by Sprint at this point in
time ,however I was unable to find any web access to said database

Keep those faxes.  According to the law, they are worth some money. 
The following is from the answer at
http://answers.google.com/answers/main?cmd=threadview&id=237909

"The following is from the Telephone Consumer Protection Act of 1991
TITLE 47 > CHAPTER 5 > SUBCHAPTER II > Part I > Sec. 227 at
http://www4.law.cornell.edu/uscode/47/227.html

"(3) Private right of action 
A person or entity may, if otherwise permitted by the laws or rules of
court of a State, bring in an appropriate court of that State -
(A) an action based on a violation of this subsection or the
regulations prescribed under this subsection to enjoin such violation,
(B) an action to recover for actual monetary loss from such a
violation, or to receive $500 in damages for each such violation,
whichever is greater, or
(C) both such actions. 
If the court finds that the defendant willfully or knowingly violated
this subsection or the regulations prescribed under this subsection,
the court may, in its discretion, increase the amount of the award to
an amount equal to not more than 3 times the amount available under
subparagraph (B) of this paragraph."

Best regards, 
journalist-ga

Greetings Tolvin:

JunkFax.org shows the 877-400-0758 number on their site at
http://www.junkfax.org/fax/profiles/faxcom.htm - this may prove to be
of help as the article there outlines that these numbers go through an
entity called Faxcom.  It's a very interesting article.

Best regards,
journalist-ga

While, in theory, you may try to exercise your legal right to collect
the penalty for receiving junk faxes, in practice it does not work.
First, no one will assist you.  I tried contacting attorney generals
and the FCC and got the same response from all "Sorry, we don't handle
individual complaints, but you are free to pursue this on your own."
So, I researched it and found out that with all of the legal wrangling
by the junk faxers, it ends up costing the victim well more than the
$500 judgement.  By the way, in the few cases where an individual has
actually made the investment and won their case, the junk faxers never
paid the judgement citing "first ammendment rights."  Also, in many
cases, companies such as fax.com ended up suing the victim and
although fax.com never won such a case, it does cost the victim the
expense of defending themself.

As a note, I meant to write FTC not FCC.

Thanks Journalist, this was what I wanted to know.

Here is an informative article about Fax.com from Wired magazine. 
http://www.wired.com/news/print/0,1294,61861,00.html

To summarize: Fax.com and its subsidiary shell or front organizations
continue to send out junk faxes, and despite considerable legal
attention, so far they appear to be beyond the reach of the law.