The Apply page for all jobs will include your company name so it won't be blind if candidates apply online. One option is to use the Apply Email address on the Launch tab to collect resumes from applicants.
If you have a place to post the job, such an external job board like Monster, Craigslist or an industry job board, you can say that applicants can send a resume to the Apply Email address for the job. When an applicant sends an email to the Apply Email for a job and attaches a resume, a candidate record with the resume will automatically be created in the system.
Note that if you have an email triggered to be sent out when a person applies, that email will likely include your company name so it wouldn't be completely blind once they've sent in their resume.
Many of our customers have posted blind job ads by creating a brand new ApplicantStack account just for their blind posting. Since there is no contract and you can pay monthly, you can just keep the account open for the month or two needed to collect your applicants and then close the account without any other fees.