Can I name a successor holder on my FHSA the way I can on a TFSA?

Generally, yes. Similar to a TFSA, an FHSA can typically have a successor holder named on it, usually a spouse or common-law partner, who takes over the account directly if you die, or a beneficiary named instead, who would receive the account's proceeds rather than continuing the plan itself. Which of these applies to your situation depends entirely on how the account is designated, so this is a real and available planning feature, not something you have to hope works out by default.

Because the FHSA is a newer type of registered plan, the exact mechanics of successor-holder and beneficiary designations, including any paperwork requirements and how they interact with a will, are worth confirming directly against the current rules rather than assuming they work identically to an older, more established plan like a TFSA in every respect. Making sure your FHSA actually has a designation in place, and that it reflects who you actually want to benefit, is a simple step that's easy to overlook when opening an account focused mainly on saving for a home rather than on estate planning.