Interesting question that you raise... so I will happily explain it :-)
"Enquirer" is a common and untrademarked name.
Enquire is a common variant of "Inquire" which is simply another common english word.
http://www.m-w.com/cgi-bin/dictionary?va=inquirers
The National Enquirer, which i assume is the print tabloid you are referring to has a trademark for "National Enquirer" but not for "Enquirer".
An Enquirer is somebody or something which "Enquires" or "Inquires".
Nobody can have a trademark for "Enquirer"... nor can anybody trademark the word "Shoe" or "Horse" or "Funny" or "Ford" or "Poster" (which incidentally would be a much more viable analogy b/c a "poster" would be somebody who "posts"... and a "xxxposter" would be somebody who posts about "xxx"... or at least i would assume so).
Now with regards to the other example above that is certain to raise an eyebrow is "Ford". Now it is important to realize that Ford Motor Company Inc. has a trademark for that term with regards to several different industries, but they do not have rights to the word "Ford" with regards to the dance industry or the mining industry... trademarks and patents are very specific.
http://tess.uspto.gov/bin/showfield?f=toc&state=ll87t9.1.1&p_search=searchss &p_L=50&BackReference=&p_plural=yes&p_s_PARA1=&p_t agrepl%7E%3A=PARA1%24LD&expr=PARA1+AND+PARA2&p_s_P ARA2 =enquirer&p_tagrepl%7E%3A=PARA2%24COMB&p_op_ALL=AN D&a_default=search&a_search=Submit+Query&a_search= Submit+Query
Just a quick legal lesson for ya ;-)))