The Chinese word for pillowcase is
枕套

zhěn tào

Chinese Definition

pillowcase
1. 枕头套
Components
枕
1. pillow
2. occipital bone
3. Alternative form of 軫 (cross board at rear of a carriage)
4. to pillow; to lay one's head on
堆屍貯積手足相xiāng 枕 - Bodies are piled up with their hands pillowing upon feet.
5. to approach
6. to lean on
7. Alternative form of 沉
套
1. to cover with; to encase; to put on (a sweater, etc.)
2. case; cover; sheath; wrapper; envelope
3. (colloquial) condom
4. to overlap; to interconnect
5. set; suit
6. knot
7. to harness
8. harness
9. trick; trap
這套拼音方案 - this romanization scheme
10. (Hokkien) Alternative form of 軀 (su, t=Classifier for sets of clothing)