Where would you insert a comma at in this sentence? One of the neighborhood cats Trina loves to play outside in the garden.

I think that a comma is needed before and after "Trina" so the sentence is: "One of our neighborhood cats, Trina, loves to play in the garden". It means that there is not only Trina but some other cats, too and we have to emphasise just the name of the cat, the word "Trina".

After Trina, loves to play outside in the garden.