That's philosophy for you. We either name it what it is, or we name it what it is in a different language.
Philosophy
Discussion of philosophy
The second part of your text I'd classify as nearly textbook subjectivism ( https://en.m.wikipedia.org/wiki/Subjectivism ).
The first part is more complicated. If I recall that debate got kicked off by Descartes with cogito ergo sum, I think therefore I am.
Then Hume followed up with questioning if a stable self exists at all and later Nietzsche who stated that what we call "I" is only a bundle of instincts and enjoying that we are too overcome.
The English names for those teachings I don't know though, sorry.
A philosopher arguing for the complete non existence of self is not known to me and it would be hard for me to follow to be honest. To freely quote a whale: who is that I that does the thinking and asking anyway?
Edit: language