On 21st December, Eddie Izzard announced that she would be using the pronouns "she" and "her" in future, because she identified as gender-fluid and was wanting to be in "girl-mode" now. She hasn't as far as I know chosen a new name, just moved to female pronouns.
A month earlier Jan Morris, who used to be James, died and received mostly respectful obituaries, having changed both gender and pronouns in the late 60s and early 70s, in a long transition as one of the first high profile transsexuals in this country.
Traditional grammar offers a small group of pronouns which differ in inflection according to number, gender and function in the sentence. But traditional grammar can't keep up with changing ideas about identity and orientation and new pronouns have entered the language:
|thon is laughing||I called thon||thons eyes gleam||that is thons||thon likes thonself|
|e is laughing||I called em||es eyes gleam||that is es||e likes emself|
(Rickter, c. 1973)
|xe is laughing||I called xem||xyr eyes gleam||that is xyrs||xe likes xemself|
|ey is laughing||I called em||eir eyes gleam||that is eirs||ey likes eirself|
|per is laughing||I called per||per eyes gleam||that is pers||per likes perself|
(Hulme, c. 1980)
|ve is laughing||I called ver||vis eyes gleam||that is vis||ve likes verself|
|hu is laughing||I called hum||hus eyes gleam||that is hus||hu likes humself|
|E is laughing||I called Em||Eir eyes gleam||that is Eirs||E likes Emself|
|ze is laughing||I called mer||zer eyes gleam||that is zers||ze likes zemself|
|ze (zie, sie) is laughing||I called hir||hir eyes gleam||that is hirs||ze (zie, sie) likes hirself|
|zhe is laughing||I called zhim||zher eyes gleam||that is zhers||zhe likes zhimself|
|sie is laughing||I called hir||hir eyes gleam||that is hirs||sie likes hirself|
|peh is laughing||I called pehm||peh's eyes gleam||that is peh's||peh likes pehself|
(anon., c. 2013)
|ze (zie, sie) is laughing||I called zir/zem||zir/zes eyes gleam||that is zirs/zes||ze (zie, sie) likes zirself/zemself|
|fae||fae is laughing||I called faer||faer eyes gleam||that is faers||fae likes faerself|
Here the sheer range is dazzling (I took the chart from Wikipedia). And there is no clue to what recent gender-identities they relate to. Non-binary, gender-fluid, pansexual, intersex, transgender people might choose to use one of the above, use traditional singular pronouns or opt for the very versatile "they, them. their" choice.
The problem is the lack of universal agreement, with such a lot of choice. But there is a movement now for people to introduce themselves by pronoun as well as name: "I'm Mary; I use she and her pronouns," "My name is Sam; I use they and them pronouns." This can only be helpful.
The new pronouns are not "gender-neutral" but "non-binary."
According to the Cambridge dictionary this can mean: the quality of including a lot of small details. "Granular" and "granularity" has become extraordinarily popular with politicians in the run up to the UK/EU Brexit trade deal.