I pronounce my first name [ˈhɛnrɪsən], which is kind of like “Henry” with a suffix “-son”. People sometimes mishear my name as “Harrison” or “Henderson”, but those are not my names. Potentially confusing is also the fact that my first name is not a patronymic; as far as I know, I do not have any ancestors who I might be named after.
By far, however, I seem to get more questions about my last name. My last name is easy if you know how to say “Thank you” in Mandarin Chinese (謝謝/谢谢) because it is simply the unreduplicated form of that expression. In Mandarin, it’s pronounced [ɕie], but [ʃjɛ], [sjɛ], or [ʃɛ] are fine approximations in English. To those unfamiliar with IPA, I usually say: “Shh” followed by a “Yeah”.
The spelling I ended up with comes from the Wade-Giles romanization system, which used to be the standard for scholarly work on Mandarin Chinese, and is the system generally used by people from Taiwan (where part of my family is from) to romanize their surnames. If my father had come from elsewhere in the Sinosphere, I could have been Henrison Xie, Henrison Tze, or Henrison Sia, to name a few possibilities. For the curious, Wikipedia has a page devoted to this surname here.