Thanks for your reply. I forgot to mention that this is an app developed overseas (not where my brand is registered). With that being said, since the app is available on Android and IOS I am not sure if this count.
Where are you located? Where is your trademark registered? Where is the app maker located?
Same name trademarks are often not a problem if the goods/services being offered are in different classes, the consumer market for the goods/services do not overlap, the geographic areas are different, and no consumer confusion is generated by the dual use.
You have, for two examples out of many, Delta airlines and Delta faucets, and ABC warehouse and ABC news. These same name trademarks are able to peacefully coexist. Consumers do not confuse one company with the other.
You say you have a fashion brand and the holder of the other trademark has a game app. On the face of it, consumers are unlikely to confuse the origin of your fashions with the origin of the game app. But a more in depth analysis would be made should the game maker actually legally challenge your use of the same mark to identify your fashion brand.
What the app maker did in notifying you of the potential conflict is what all diligent trademark holders should do. It is up to the trademark holder to police the marketplace for possible infringers and enforce their rights. There is the risk of losing all rights to a mark if the trademark holder lets others use the same name with impunity.
Avoiding a trademark challenge is always the best course of action when this is possible. If you are wedded to your name, you can wait to see what happens. Or, the f you want to rest easy, you can change your name to one not owned already by someone else.
As an additional note: In many other countries, the registrant of a mark will be the presumed owner of the mark. In the US, registration is not necessary and if will be the first user of a mark who is the presumed owner. This is a rebuttable presumption.