Pursuant to TMEP 1211.01, a registration can not be issued wherein the mark comprises "primarily merely a surname".  In determining this, the USPTO looks to five factors:

(1) whether the surname is rare (see TMEP §1211.01(a)(v));
(2) whether the term is the surname of anyone connected with the applicant;
(3) whether the term has any recognized meaning other than as a surname (see TMEP §§1211.01(a)–1211.01(a)(vii));
(4) whether it has the “look and feel” of a surname (see TMEP §1211.01(a)(vi)); and
(5) whether the stylization of lettering is distinctive enough to create a separate commercial impression (see TMEP §1211.01(b)(ii)).
In re Benthin Mgmt. GmbH, 37 USPQ2d 1332, 1333-1334 (TTAB 1995)

Here:

(1) the examining attorney submitted that BARR appears as a surname 13,622 times in the Lexis telephone directory listing;
(2) a Mr. Michael Barr is an active participant of the BARR GROUP's activities;
(3) the Board observed that all marks consisting of the term BARR were registered with a claim of acquired disetinctiveness, and does not engender the a "consumer preception beyond that of a surname";
(4)-(5) not applicable as the mark here is a word mark registration.

Because all the factors weighed against the Applicant, the Board found that the term BARR GROUP was primarily merely a surname, and affirmed the refusal of the registration.

However, it should be noted that not all surnames are rejected categorically, as the emphasis of TMEP 1201.1 is hinged on finding that the applicant mark is primarily merely a surname. For instance, rare surnames pursuant to TMEP 1211.01(A)(V) may be allowed for registration if the factors above weigh in favor of the applicant.

For the full opinion -- http://ttabvue.uspto.gov/ttabvue/ttabvue-86140341-EXA-13.pdf