Writing a cover letter for a no name

Are you applying via a resume drop or by email?

In this case, I'm assuming you are asking if there are any opportunities available, rather than applying for a specific position. If that is the case, I would advise that you draft a Letter of Inquiry, which is similar to a cover letter, but instead of focusing on a specific position, it focuses on opportunities within a particular firm that, given your background, you would be a great fit with.

In this case you need to do as much research as you can (yes, I know it is often hard to find quality info, even on their sites) - do Google searches and such for any deals, news articles, etc - and then focus your cover letter on the strengths of the firm and the strengths of yourself. Essentially, it should be similar to a cover letter in that you should introduce yourself and touch on your background. Then you need to site specific examples that support yourself as a strong candidate. Finally, you need to express an interest in working for the firm in a specific capacity. Close it with the usual closing phrases, and if they have a phone number, let them know that you will follow up via telephone call at such and such time in the near future.

If, however, you are writing the standard cover letter and applying through a resume drop, then work with your standard cover letter. Use Google searches to find anything you can to highlight your knowledge of and interest in the firm, and, again, if possible, follow up with the phone call.

Good luck and let me know if you have any other questions.