No, the registered name of the store is used by others before it can be considered as an infringement, but it depends on what kind of registered trademark it is. The general trademark used as the name of the store is not an infringement, but if it is a well-known trademark, even if the trademark and the trade name are two different things.

Legal basis:

Article 52 of the Trademark Law Any of the following acts of trademark infringement is an infringement of the exclusive right to use a registered trademark:

(1) Using a trademark identical with or similar to its registered trademark on the same commodity or similar commodity without the permission of the trademark registrant;

it is not infringement that the name of the store is used by the owner, because the party concerned has not registered the copyright of the store name, so it is allowed to have the same name, and it is not allowed to ask the other party not to use the name.