Is it OK to Omit My Current Company's Name on a Resume?
What do you put on a resume when you do not want to put the name of your current company?
Your resume should be an accurate reflection of your work history and skills. You simply cannot omit the name of your current employer. Saying who you work for says something to a prospective employer about who you are and what type of work you do. You won't benefit in any way from hiding this information.
If your concern is that you don't want your current employer to know you are looking for a job, then that's a common request from job hunters and is understood and accepted by most recruiters. Simply tell them you do not want your current employer contacted before a job offer has been made.
Of course, you'll also need to likely agree to the fact that your job offer may be contingent upon a positive job reference from your current employer.
Put your request directly in the cover letter, saying something like, "My current employer is unaware that I am looking for a new job, so please do not contact them without my permission."
Good luck with your hunt!