Question: My comic has the name of an existing record store. Am I in trouble for possible copyrights infringements?
Answer: The issue is related to trademarks which protect the name of company, a service, or a product. A comic itself is not a trademark. It is protected by copyrights. The title of your comic is the thing protected by trademark.
Now, you mentioned that the other company using the name is a record store. If this store has trademarked its name, it will be protected under what is known as a class of wares. Wares are the product type and category where they want to protect their name. The wares they have reserved are probably related to store, music, records and so on. I highly doubt that they have protected their names under wares related to comics - in the US there are specific wares for comics - more than one actually.
If they have not protected their trademark for comic-related wares, then they cannot stop you from using the name.
For example, think of a company called Igloo Frozen Yogurt and another one called Igloo Ventilators. Each of these two fictional companies may have trademarks for the name Igloo but because the word "igloo" is generic, they cannot claim exclusive usage of this name and probably have only selected a few wares. If the wares do not overlap, each company can continue to use the trademark igloo in their respective business spheres.
Here is another real example. We all know about the hero Aquaman. Well, there is a perfume called Aquaman made by another company. Even though one would think the name Aquaman is quite well-known in comics and entertainment, DC Comics not having reserved the wares for perfumes cannot force the cosmetic company from producing and marketing a perfume called Aquaman.
P.S. I am not a lawyer. For best information regarding your case, ask a lawyer!