According to my copy of Burnham's Celestial Handbook, volume 1, 1978 published by Dover Books, Sirius has been translated as 'The Sparkling One', 'The Scorching One', and is also called Sothis, the 'Star of Isis' by the Ancient Egyptians, among a very large list of names including the Dog Star ( Alpha Canes Majoris).
Procyon (Alpha Canes Minoris) also has a long list of names including Antecanis, 'Before the Dog' and the 'Little Dog Star'. Procyon rises before Sirius which is why it gets names like 'Before the Dog'. So, Sirius has a long list of names that highlight many facets to its identity including the fact that it is THE Dog Star. Procyon's claim to fame is that it rises just before Sirius so that's probably why it's name explicitly includes reference to its doggy nature!