Recruiters care very much about your current or most recent employer. Why? Because the fact that you work for that employers means you have an understanding of a specific industry space. Or because that employer has a history of hiring great talent. For these reasons, company names are frequently used as keywords in recruiters search engine strings. When it comes to searching, I have found that recruiters tend to fall into one of two camps: the broad searchers who gradually narrow their search results (starting with a big slate of candidates and filtering it down manually), or the narrow searchers who broaden their search results (by doing multiple searches) until they fill out their slate (I'm the latter, by the way). Either way, thinking about how you refer to your company on your resume is important, otherwise, you may not attract the recruiters that are looking for someone just like you (though you may attract the ones that are looking for someone kind of like you; those recruiters matter less). So a couple of tips for you that I have used or learned from other recruiters:
-When you refer to your company, spell it out, abbreviate it and describe it. For example, IBM might be IBM or I.B.M or International Business Machines. The best recruiters will have something in their search string that looks like this: AND (IBM OR I.B.M. OR "international Business Machines").
- I love this one. For a recruiter to do a web search including your current employer as a keyword, they may do something like this: AND Starbucks NEAR (Present OR Current). This means that the employer name of Starbucks is near the words "current" or "present" on the resume. Different search engines have different roles about what "near" means. I have seen job seekers use many different terms to describe the tenure of their current position; wording like "-til date" (which isn't even correct grammar) and "til now" (too conversational). See that all the time. I would definitely suggest using the words "current" or "present" to describe the tenure of your current position and I would definitely make sure that they fall within close proximity of your company name.
Some recruiters really get into Boolean logic and I admit that I am a little out of practice, but as I hear about these little tips and tricks, I will pass them along.