The Nike swoop on athletic gear, for example, identifies the gear as coming from a specific source: Nike.
Trademarks can be whimsical words or phrases, sounds, or images, or whole design schemes (McDonals's arches; the coke bottle shape and stylistic logo). But the bottom line is that it has to identify the source, not describe the product.
In most countries, trademarks are established by use (registration is just a recognition of rights you established by using the mark to identify your company as a source of the goods). So, in a system like that as long as you has been using the mark, have paid the registration fee and jumped through the proper hoops, you are entitled to the registration of the mark. (Some of the hoops are related to the nature of the mark, others are related to not infringing a mark previously used by another for the same class of goods).
You are only entitled to the mark if you are using it as a source identifier for the class of goods for which it was registered (or for a limited time before registration have an intent to use it).
I believe the system in China is broader - and proof of actual use is not required to obtain the mark (only to avoid cancellation in certain circumstances) I don't know Chinese trademark law enough to know whether they "have to" register her marks if she jumps through certain hoops - or have the discretion to deny it.
Any marks she registers in China are valid only in China.
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