Honor Those Who Served Act of 2014 - Authorizes the following persons to request a headstone or marker to be furnished by the Secretary of Veterans Affairs (VA) to commemorate an eligible decedent:

• the decedent's next of kin;
• a person authorized in writing by the decedent's next of kin to make such request;
• a personal representative authorized in writing by the decedent to make such request;
• in the case of a decedent for which no such person may be identified, a state veterans service agency, a military researcher, a local historian, or a genealogist or other person familiar with the research sources and methods necessary to prove the identity of the decedent; or
• in the case of a decedent who is a veteran who served on active duty in the Armed Forces at least 75 years before the date on which the headstone or marker is requested, any person (subject to a request by the decedent's next of kin to change the placement of, or to remove, such headstone or marker).

Permits the last two categories of persons to request emblems of belief for such a headstone or marker only when such a person can provide sufficient evidence regarding the decedent's religious beliefs.