I would not name a cat Tigger because you could be misunderstood and offend people when you are calling him. Tiger would be OK, or Tyger if you are a fan of William Blake.
I am offended for SC that people would think he is a bad owner. A happy cat is one that is free to spend his time inside and out. Given the choice they seem to like a 50/50 split, often they like being outside when the humans are at work and school, inside in the early morning and evening, and overnight depending on the weather.