I have register a domain name for my personal portfolio site. I am making custom products and i would like to use my domain name on my custom products. For example xxxxxxx.com. Exactly this name with the .com at the end it will be on my custom products. If someone registers the xxxxxx name am i going to have a problem? Can i use my web address on my custom products?
In the US, assuming that is where you are, trademark rights are developed by using the trademark, not by registering it. The first business to use the trademark appropriately as a trademark (and continues to use it) has first rights in it. Registration gives the owner extra rights and makes it easier to enforce all the owner's trademark rights, but the initial right in the trademark comes from using it. Also, the standard for trademark infringement is the question of whether there is a "likelihood of confusion."
So the important question is whether anyone else in a similar line of business to you is using a similar mark -- not just an identical one. Similarity of the marks depends on the overall commercial impression people get from the mark, and can include marks that sound similar or look similar and even sometimes
just have similar meanings.
Before using your domain name as a trademark, it would be wise to have a trademark search done by a trademark attorney, who will know what to look for in conflicting marks that may be "similar" but not identical. The attorney would also know to check both the Federal Register and other sources, in case there are unregistered trademarks which may have priority over yours.
After checking to see if you can find any other business similar to yours with a similar mark, if it seems you will be the first to use it, you can start the registration process if you like. If you have not yet used the mark in interstate commerce, you may begin the registration process using an "intent-to-use" application. Registration will not issue until you have used the mark in interstate commerce, but you will get the date you file your application as a priority date, so if anyone else begins using a similar mark after your application goes in, you will still have priority over them.
Sorry for my bad english.
No need to apologize. Your English is better than the English we see from many native speakers these days!