I don't think you can have "implied rules" that stand up in court. There's a rule, or there isn't. And I'm not aware of any rules about how you name your network.
What counts are the rules that you apply for membership: if you let only some men in and not others, that's potentially unlawfully discriminatory. If you let all men in, or no men, you're on safer ground. The title of your organization can be, but is not necessarily, the same as the rules of membership. A "Women's Network" that openly admits all men regardless of how they identify, is not breaking any rules.
Both the Women's Institute and GirlGuiding were forced to restrict their membership to Women and Girls respectively because doing otherwise would have mean not just rewriting their Rules but also changing their name.
I don't think that's true. Although neither the WI nor GG has released the legal advice that made them take the action of becoming single-sex associations, there's nothing to suggest it's because of the name. It's widely supposed (and I agree) that the significant legal hurdle is that the charitable purposes of those two organizations prevent them from benefiting other than women and girls. I'm fairly confident if all it took to permit men (or boys) to become members of either organization was a name change, that would be done lickety-split. The Boy Scouts Association changed it's name to The Scouts Association in 1967, I'm told, and it's royal charter (to admit girls) in 1991. The two are different matters.
It's possible for a workplace network to be both an association and also part of an employer's duty not unlawfully to discriminate. The choice of which tack to take would be down to the person complaining of discrimination. Do you want to take the employer to court, or the network itself (which may not in fact have a legal personality)?
This is not a moot question: you'll recognize that SEEN very unusually formed a corporate body when it looked like it was facing legal action from Tempest; one might guess this is to shield its individual members from personal liablility. In the end DEFRA was the defendant.