A search for Hinchey with birth location keyword Clare produces these 12 hits:
* Hinchey x 2
* Hinchy x 10
A search for Henchey with birth location keyword Clare produces these 4 hits:
* Henchey x 1
* Hinchey x 2
* Hinchy x 1
It is conceivable that Hinchey and Hinchy are considered synonyms for Henchey, but not vice versa.
But why is one of the Hinchys considered a synonym for Henchey, but not the other nine Hinchys?
The best-known spelling is probably Henchy, with five notables, one born in Clare, at
https://en.wikipedia.org/wiki/Henchy
A final search for Henchy with birth location keyword Clare produces these equally perplexing 4 hits:
* Hennessy x 1
* Hinchey x 2
* Hinchy x 1