"내가 갖고싶는 이름을 몰라." First, 싶는 is wrong. 싶다 (wanting to do something) is an adjective (auxiliary adjective to be exact, because it needs a verb before it in the -고 form), and adjectives can't take the -는 conjugation form. The -는 connective ending indicates a progressing action and only applies to verbs since adjectives can't represent an action (with a few exceptions like 있다 and 없다). Secondly, 갖고 싶은 이름을 몰라 sounds like you already have a name you want but don't know what it is (which doesn't make sense), rather than not being able to decide on the name. To express the latter, we say 어떤 이름을 갖고 싶은지 (what name I want to have). Thirdly, 몰라 means a clear cut "I don't know". When you're unsure of something, the -겠어 (maybe I might as well ...l, can't seem to ..., etc) ending makes it softer and more undecided. Hence 내가 어떤 이름을 갖고 싶은지 모르겠어.

So if you correct your grammar, and say 내가 갖고 싶은 이름을 몰라. Native Korean probably understand what you mean, but it sounds a little bit awkward. It's not korean way to express it. So your best bet is to say 내가 어떤/무슨 이름을 갖고 싶은지 모르겠어 *verb + 고 싶은지 Its somehow complicated to explain in grammar, so I'm going to give you some examples I'm not sure what I want to eat 내가 뭘 먹고 싶은지 모르겠어 I'm not sure where I want to go 내가 어디에 가고 싶은지 모르겠어

In the first sentence that you wrote, you misspelled one '하고 싶는(x) 하고 싶은(o)' If there is a hanguel at the bottom like 싶, you should put '은' behind the word. But if the one without the bottom like "친애하는" which means 'dear my~', you should put '는' behind the word