If your use of the name predates the other company's registration and use in your marketing area, then you actually have priority rights over the other company regardless of the registration. In trademark law, the registration provides a holder of the mark with presumptive rights - meaning it is "presumed" that the holder has priority rights. This presumption can be disputed by a person or company using the name prior to the registration. Therefore, if you used the name PurpleWidgets.com in the marketplace prior to their registration of "Widgets", then you have the priority rights.
Assuming that their registration occurred prior to your use of the name, then the next question is whether the name causes "confusion in the marketplace". In other words, are both uses for the same types of products or services so that consumers or customers would be confused as to which company is which? Is confusion with the other company likely to occur by their customers or yours?
As you can discern, trademark law is complex and the answer to your query requires a bit more information.
If you would like to call me to discuss this, please feel free to call me at 215-525-1165 x101.
If you found this response useful, please mark it as a "best answer".
This response does not create an attorney-client relationship and is not intended to provide legal advice for your specific situation.
Before I respond to your inquiry, I must state that we have not spoken, I have not reviewed the relevant documents and facts, and I do not represent you. Therefore, my discussion below is not a legal opinion, but is informational only. Finally, my discussion applies only to issues to which Pennsylvania, New Jersey or Federal law apply, unless otherwise specified.
That being said, Ms. Lanard gave you a good answer. I would add that if you do not refer to your product as a "Widget" to your customers, but are using the name "widget" in your company name and website, AND the competitor DOES use the name "Widget" for its products, you may have a problem with an unfair trade practice under the PA Unfair Trade Practices and Consumer Protection Law, which is designed to protect consumers and competitors from unfairly deceptive or confusing branding and other practices. I suspect that you don't need the 'widget' name to market your product; if your company grows, you may even find that it limits you.
/Christopher E. Ezold/
The Ezold Law Firm, P.C.
One Belmont Avenue,
Bala Cynwyd, PA 19004
First, one quibble with my colleague's analysis: The first one to use a trademark in commerce is the presumptive exclusive owner of the mark when used to brand the marked goods. So the two relevant dates to determine whether you or the other company is the senior user of WIDGET are the dates of your respective first uses of WIDGET -- the date the other company registered its mark is not relevant when determining which of you has priority rights in WIDGET.
If the other company used its mark first then it's the presumptive senior user and, therefore, the owner of the mark [as used to brand the mark goods]. If it used its mark first AND registered it before you began your use of your trade name then the statutory benefits granted to trademark registrants apply and the other company has even more arrows in its quiver if it tries to enforce its trademark rights against you.
If you used your trade name first but the other company registered its mark first then you and your own trademark attorney need to consider whether that other company's use of its mark infringes your trade name. If yes, then you should considering attempting to cancel the other company's trademark registration -- or simply ignore the registration or suggest a concurrent or consent to use agreement with the other company or something else creative.
Second, your company's name is Purple Widgets, Inc., publishes a website at PurpleWidgets.com and sells Widgets but "[w]e do not refer to our products as Widgets ... ." That sounds very odd. What do you call your Widgets? Don't answer -- speak to your own trademark attorney about the matter. Good luck.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
One further note of enlightenment. There are 2 ways to get priority on a trademark, (1) use it first, or (2) apply for a US trademark registration before anyone else uses the mark.
(1) was mentioned in several answers. I won't burden you by repetition of them.
As to (2): One answer (which you marked "Best") suggested prior registration might give priority, but it is the filing of the application that confers priority not the registration, and that is only true if the registration ultimately issues, and (sorry for the run on sentence) it only registers if you apply, the application is allowed, and you prove you have used the mark in commerce and you do all that in the proper manner.
If that confuses you, the message is that you need to see a trademark lawyer and get some specific advice. The use of "Widget" and the other "hypothetical" facts render it hard to give specific advice. You need to give those facts in confidence to a trademark lawyer. Look at the answers and pick your lawyer and go get that advice, and do it soon.
Best of Luck.
So far, this is free to you. Until you pay a fee, I am not your lawyer and you are not my client, so you take any free advice at your sole risk. I am licensed in IL, MO, TX and am a Reg. Pat. Atty. so advice in any other jurisdiction is general advice and should be confirmed with an attorney licensed in that jurisdiction.