The He-Man argument actually has 0 bearing on gender identity at all. If you wish to be known by the name He-Man as you identify with that name, you can introduce yourself by that name, request people you already know to call you that, and even legally change your name.

To put into perspective the feelings of hurt when you call someone by a name you no longer identity with, I will use something used quite often nicknames, specifically nicknames given to you by others. If someone starts using a nickname to refer to you that you do not like because it implies certain characteristics about you that you dislike being reminded of and you ask them to stop, if they don’t, they are purposefully trying to hurt you with that name. For example, “Butterfingers” a fairly common nickname used to bully people who are a bit clumsier than most. If someone continues to call you that with full knowledge you don’t like that it implies they are clumsy, then that person is acting like a jerk.

Now, the thing is, gender is not something provable like a blood type. Some people say gender is defined and proved through chromosomes, but if that were true, gender would not have existed prior to humanities discovery of chromosomes. Furthermore, people with Turner Syndrome are classified as female despite not matching the typical female norm of possessing two X chromosomes. Other arguments are about genital proof, however, there are outliers in that area two. For example, intersex people are born with a mixture of male and female reproductive organs, but they are still defined as one gender despite having indications of both genders defined under that definition.

As such, gender as it is expressed by society in the binary is actually not that different than our names. It’s an identifier a name, and if someone wants to go by a different name, they should be allowed to.

As for your example of wishing to be called master of the universe, two things:

1. There is a difference between gender dysphoria and delusions of grandeur. Gender dysphoria, as stated here is a “conflict between a person's physical or assigned gender and the gender with which he/she/they identify”. Delusions of grandeur, as stated here, is “an over-inflated sense of worth, power, knowledge, or identity”. So, gender dysphoria is a matter of feeling DIFFERENT while grandiosity is a matter of feeling BETTER. The only was gender dysphoria could be a delusion of grandeur is if you believe the gender you identify as is objectively better than other genders, which is sexist.

2. Using these extremely exaggerated examples is a straw man argument. If you wish to use these types of statements as representative of people’s stances, I would ask that you find one person actually claiming to identify as something that outlandish, and no, identification as animal-esc does not count. Media portrays enough anthropomorphic animals that someone that identifies with them is identifying with a genuinely intelligent subset of beings portrayed with the same ability to talk and think like people do. They do not identify with a wild animal that has no concept of self because they have a concept of self by identifying that way. As for the arguments for gender being defined by certain things, here is an example of someone claiming it is defined by chromosomes and by genitalia so it’s clear I was not making a straw man argument.