The facetious suggestions of "Isle of Person" and "Isle of Perdaughter" as replacements for "Isle of Man" are based on both an etymological fallacy and a reality-based one.
The etymological fallacy is highlighted by the Wikipedia article
about the island:
"The name is probably cognate with the Welsh name of the island of Anglesey, Ynys Môn, usually derived from a Celtic word for 'mountain' (reflected in Welsh mynydd, Breton menez, and Scottish Gaelic monadh), from a Proto-Celtic *moniyos."
So the origin of the name has nothing to do with males, or even with 'man' as a shorthand way of referring to humankind.
The reality-based fallacy is the assertion that anyone might genuinely propose changing the name of the island because it does not match their desire for "political correctness".
A comment I came across on Quora puts that point rather well:
"I have never heard of anyone suggesting this. What it sounds a bit like is the sort of straw-man nonsense about PC Gone Mad that you hear from time to time. ‘You’ll never guess what the FEMINISTS want to do now!’ (99% of the time, no, they don’t.)
If nothing else, the idea that feminists basically want to take the three letters MAN and replace them with WOMAN wherever they appear is an absurdly dumb and incoherent idea of what feminism actually is."
This is borne out by the actual focus of the activist feminists I know (and I know many), which is targeted on issues of genuine societal concern and has no connection with the caricature of feminism implied by this trivializing nonsense about renaming the Isle of Man. It includes their attempts (not least through the sponsoring of suitable legislation) to oppose people-trafficking and sexual slavery (including the exploitation of women by pornographers); prostitution; child surrogacy; female genital mutilation; sexual harassment, such as takes place in the workplace or in the street; domestic violence, and misogyny in general; and to promote the legally-enforceable equality of treatment for men and women in societal institutions.
They are also deeply opposed to the pernicious trans-activist agenda (which is heavily backed by US pharma and healthcare interests, which stand to gain financially from the associated surgical procedures and indefinite dependency on body-altering drugs) of encouraging children to reject the fact of their own biological sex, and of creating a legislative pathway (via so-called 'gender identity' or 'gender recognition' legislation) for transforming the specious notion that biological males can be female (and vice versa)
from a biological impossibility to a legal fact -- something that in the UK and too many other countries to list here is in the process of reversing most of the gains in women's rights achieved since the 1960s, and particularly infringes the rights of lesbians.
Feminism of this kind is actually a movement for promoting general human rights that is being led by women, and for this reason is especially disparaged by patriarchal men who resist changing their misogynistic attitudes -- not least because many of them want to continue enjoying their unearned privileges and de facto
ability to abuse others for their own benefit.