The Bayer designations Y Puppis and y Puppis are distinct and refer to many different stars in the constellation Puppis:
For Y Puppis:

• Y Puppis, (21 G. Puppis, HR 2642), formerly called V Puppis (not variable)

For y Puppis:

• y¹ Puppis, (98 G. Puppis, HD 59635), more commonly called y Puppis
• y² Puppis, (HD 61391, 130 G. Puppis), sometimes referred as Y Puppis as a Bayer designation
• y³ Puppis, (MY Puppis, 142 G. Puppis), a δ Cephei variable, sometimes referred as Y Puppis as a variable star designation