Vignette answers are a function of both the actual level of the person in the vignette (θ, the same for all respondents) and the DIF applied by each respondent (differing over respondents). We can think of these answers as responses to the portions of the vignette text that are, respectively, (1) an integral part of describing θ and (2) words used to package these concepts. DIF is generated by the packaging, which human language of course prevents us from eliminating entirely. Fortunately, to meet the assumption of the model, we need not eliminate DIF. We only need to ensure that the DIF each respondent applies in answering the vignette question is the same as the DIF he or she applies in answering the self-assessment question. As such, the goal of writing vignette questions is to keep θ accurately described (and distinct from the actual level of the self-assessment, μ), while making the packaging for each vignette close to the description of each respondent so that the DIF will be the same. Normally this is done by excluding age and as much of the other packaging-related information as possible and letting or explicitly encouraging the respondent to think of the vignette as describing a person like them, aside from the difference between θ (for the vignette) and μ (for themselves).
The implied sex of the name of the person described in the vignette is an issue, since ideally this would be the same as the respondent. Thus, if possible, we prefer the names on the vignettes be changed to match the sex of the respondent. When this is impossible or too expensive, using gender neutral names (Lee, Pat, Terry, Kelly, Leslie, Hillary, Bobby, Chris, etc.) or, in some languages, intials (G.K., T.R., B.C., etc.) may be reasonable substitutes.
In principle, we might think about going another step and writing the packaging to reference the respondent explicitly (e.g., ``Suppose you were paralyzed from the neck down...''). Unfortunately, self-referential vignettes ask the respondent to do research for us in constructing the counterfactual, which in many areas does not work well (e.g., it is similarly not a good practice to ask the respondent for the causal effect of education on his or her income; a better strategy is to ask for education and income and to leave it to the researcher to estimate the causal effect). Asking a respondent to construct a counterfactual, by holding constant some aspects of themselves and changing others may be outside the experiences and beyond the capabilities of many people not trained as social scientists.
In addition, respondents in many cultures seem to respond superstitiously or overly optimistically to counterfactual situations where bad things happen to them, and they give answers that are more extreme than we would expect. In our experience, response rates and test-retest reliability also tend to drop when individuals are asked to imagine suffering bad or unpleasant health conditions. Our alternative is for the vignette to describe a different person like themselves (which we ensure they understand by using a specific named person in the vignette) rather than some counterfactual version of themselves.
An alternative would be to change the vignettes on the fly in a CATI system so that the packaging is extensive and explicitly equivalent to what we learned about the respondent from previous questions (``Bob is a 26 year old plumber from the South Dakota...''), but then the fiction of using a different name becomes more and more tenuous. In our experimentation, and cognitive debriefing, we have found that doing this is almost the same in the respondent's mind as explicitly describing the respondent in the vignette, and it does not work for the same reason. The best option, therefore, seems to be the approach of describing the people in the vignettes as people like the respondent.