To deal with the small sample size, it seems natural to want to estimate parameters across the full population (using HB), but also to customize the design (the brands seen) to be those relevant to each respondent.
When you use a constructed list in ACBC to customize the levels to be those relevant to the respondent, you have the choice as an analyst regarding how missing levels to each respondent are handled: missing at random, missing inferior, or missing unavailable. (See documentation for details, though "missing unavailable" is the most extreme way to deal with missing levels...meaning their utility is set to be most different (lower) from "included" levels for each respondent). If your client’s brand is available in all regions, then it would appropriately be handled as such in the design. If a conjoint study artificially builds awareness for each brand in the survey, then it is possible it could get an artificial leg up on the other brands due to its availability for all respondents.
I would recommend using region as a covariate in the estimation.