You need to contact an attorney now, have the attorney evaluate the marks and any facts that you have, and have your counsel respond to this person making threats. I think ignoring it and hoping the issues goes away would just be silly.
A valid cease and desist threat is a valid threat no matter how you get it, and don't kid yourself about pretending you didn't get it.
You do need to see an IP lawyer. They can review your particular sitautaion and advise you if you're best off just changing the name of your business and website, perhaps by adding a word or two to the name to distinguish it from your competitors, and they can help you pick an available and protectible name that you can trademark. Re-branding your business now would be relatively easy since it's new and you haven't invested very much.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
There's nothing legal or illegal about any of it.
You should, as has been suggested above, contact an attorney for a review of your situation, and discuss a detailed response. It's always better to spend a little money attempting to head off litigation rather than spending a lot of money on the litigation itself.
Remember that your company can not represent itself in court, and you'll have to hire a lawyer if you are sued. The cost of a consultation with an intellectual property attorney will invariably be less than the cost of fighting a lawsuit - even if the lawsuit is frivolous.
If I can be of help, please feel free to get in touch.
It doesn't matter how you got the cease and desist letter -- in fact it may not even matter if you did at all. If you have infringed a trademark you can be sued without getting a warning.
You need to see a lawyer unless you decide simply to surrender to the other side.