As long as the title says something of the same style, it is very likely to be judged as a fake by the system.
There is no need to consider whether it is an infringement. This situation is a situation where you admit to selling counterfeit goods. If you catch it, you can be punished directly for selling counterfeit goods.
What you emphasize is that the things purchased on behalf of others are considered infringement at most, but in fact they will be treated as counterfeit products.
Extended information:
Whether adding words before and after the brand name in the Taobao title constitutes infringement depends on whether it will mislead the public. ?
Article 58 of the "Trademark Law" stipulates: "Whoever uses someone else's registered trademark or unregistered well-known trademark as a trade name in a company name to mislead the public and constitute unfair competition shall be punished in accordance with the provisions of the People's Republic of China *** and the Anti-Unfair Competition Law of the People’s Republic of China”
According to the above provisions, if the words before and after the Taobao title and brand name mislead the public, it is an act of unfair competition and is illegal. It is an infringement, but if it does not mislead the public, it is not an infringement and is not illegal.
Reference materials: Baidu Encyclopedia Trademark Law of the People’s Republic of China