I think the crux of the issue is 'gender identity' overriding/extinguishing the category of 'sex' in law and policy.
All of the other issues - single-sex spaces, sex segregation in prison, sports, data collection, etc. - flow from that.
So the central mission of the party should be to campaign to retain biological sex as a meaningful legal category, and to argue that sex, not 'gender identity' should be the determinant of who gets to use spaces, services, programs, etc, that are segregated by sex, because the very logic of their existence is predicated on the material reality of sexed bodies, not people's subjective internal states.
So you need to focus on that - to draw the public's attention to the fact that politicians and policy makers are replacing the objective category of sex with the entirely subjective feeling of 'gender identity', and that this makes no sense from a legal or policy standpoint. They need to be forced to answer WHY they are doing this (who benefits, and who loses?) and to fully grapple with the wide-ranging consequences of this radical change, including the extensive safeguarding issues it will give rise to, instead of being allowed to slip it in under the guise of 'inclusivity'.
A name like SexNotGender would efficiently convey the central mission of the party, as well as allowing representatives to push for a broader examination of the logic of gender identity ideology itself,* such as the way it conflates sex (male/female) with gender/sex roles (masculinity/femininity), and the fact that the paediatric transition industry is carrying out ever more extreme medical interventions in the bodies of children on the basis of the entirely unscientific belief that they have the 'soul' of the opposite sex trapped inside their bodies.
*Imagine: every time a rep is asked to explain the name, they'd get to do a mini-spiel on how 'gender' is sexist bollocks, while sex is a material reality.