A token’s name is its subtypes plus the word “Token” unless it’s copying another object or it was given a specific name by the effect that created it. For example, Myr tokens are named “Myr Token,” and they have a different name than Phyrexian Myr tokens, which are named “Phyrexian Myr Token.”

To determine the number of differently named artifact tokens you control, count each artifact token you control once, but only if its English name isn’t exactly the same as another artifact token you’ve already counted this way.