I went to an Esperanto meeting in Canada one time and there was a fellow there who didn't Esperantize his name. His name was not one I've heard before or since, it did not end in O, and it contained at least two sounds that are not found in English or Esperanto. As the evening progressed, I watched several people come in, introduce themselves to this man, ask him to repeat his name at least once, and then finally conclude with "oh" - obvious that they've given up on trying to catch it.
This is the moment I always think of when I hear people say they're against the Esperantizing of names. We anglicize names all the time. I'm sure this man's grandson or great grandson, if named after him, would pronounce their name using only sounds that Canadians are familiar with. It's the same thing with Esperanto.
In the end it's just a question of how much effort you and your new acquaintances want to put into learning your name correctly. Same with Chinese, Polish or whatever names, you can try to teach them or just go as Jenny / Chris / ..
In other words, there are good reasons and examples for both options and it depends on circumstances what option you choose. Even if you go with your real name, most languages tend to at least pronounce it only with native sounds or sound combinations, if not spell it phonetically, and there are other languages that add endings to names already in the nominative, e.g. Latvian
I think you're saying the same thing that I am, although I would underscore that the phrase "how much effort" should not imply that simply throwing effort at the problem will not solve it.
It seems to me that the Icelandic Esperantist in Canada was not making the proper effort to speak his name with Esperanto sounds. The people he met were making a big effort but with no success. It shouldn't be necessary to learn a new language to say someone's name.
Along these lines, I met an Esperantist named Sten. He said he's gotten used to how Esperantists say his name because in his language, there are at least two different E sounds that sound different to his hear. When it's said with the wrong E sound, it sounds the same to others but as different as "Stone" and "Stan" to us. I learned how to say the difference while I was with him. It was a bit like this scene from Babylon 5 (you can skip the first 50 seconds of space scenes and still get the point.)
Finally, there was a time in my life when everybody called me Thos. It's an easy name -- starts out like "Thought" but rhymes with "Toss." Nobody ever had a problem with it. However, when I started working and meeting new people every day, I started going by "Thomas" because it was really too much to have to explain a dozen times a day.
For that matter, when speaking German, it never once occurred to me to say "it's Tɑməs, not TOE-mahss". That is, Germans always pronounce my name the German way, not the American way, so that's what I do while speaking German.
In japanese, often native-English speakers alter their names because Japanese language conventions makes it difficult for them to pronounce words with multiple consonants together. and viceversa, Japanese people often have an 'English' name. A Thai friend of mine has an English name, because some sounds, even if they use English letters, don't translate. Especially since her name had a tone in it.
In Esperanto people try to make their names more phonetic, and all nouns are meant to end with an O. My names Brian, since there shouldn't be blends in names I'm still trying to decide on mine.... Maybe Biriano, or like my Chinese boss says "Bin", but with an O on the end..... :D
Julian (My name) would be Juliano, but what would be my nickname? Juĉjo or Juliĉjo? And what if you have a name ending with a vowel? Adèle (My mothers name) would be Adèla or Adèlo and Adènjo as a nickname, right? Jelle would be Jello and Jeĉjo, right?
Also, names for men 'generally' end with an 'o' in Esperanto, so what are some other opportunities?