If your name is supposed to appear in legal documents such as a passport, your name will be spelled in German documents exactly as it is spelled in the documents of your home country. If a transliteration (from a non-Latin to the Latin alphabet) is necessary, the transliteration follows ISO norms. You cannot choose the spelling of your name.
You can legally change your name only if the name causes you serious disadvantage, for example if it has an obscene meaning and you are being harassed for it. Difficulties in pronunciation and spelling can be a reason for changing your name, if the handicap caused by it is "not insignificant". It is unlikely, though, that you will be allowed a spelling of your name that is equally or almost as difficult as the original one.
If you use your name in documents such as contracts or certificates, it must be written exactly as it appears in your passport, otherwise the document may not be legally valid.
Everywhere else (that is, outside of legal contexts), you can write your name however you want.
There are German names that are written with a diaeresis, such as Piëch or Meÿer, foreign names that are written with a diaeresis in German, such as Noëlle or Croÿ, and so on, so the use of the diaeresis will be familiar to some Germans. Unfortunately the diaeresis does not always signal a vowel hiatus in German above a y, so that spelling will not clearly indicate the pronunciation of your name for most Germans. (See the answer by Hubert Schölnast for more details on this.)
Given the many names of foreign origin in Germany today, many people have to explain the pronunciation of their names. My own name is not German in origin and everyone who sees it for the first time asks me how it is pronounced. It doesn't bother me at all.