Please, consider this:
I too was given a "unique" name. It isn't as extreme as to contain foreign diacritical marks (thank God), but it is extremely rare; I've only met one person with the same name in my entire life. It is rare enough to sound non-conventional, foreign, and just plain weird to most people.
When I was in my early teens, I experienced the reality of living in a world where my peers make fun of my name - "Why can't you have a normal name?", "What kind of name is that?". The bullies didn't even have to come up with a clever way of calling me names; the teachers did it for them by constantly either mispronouncing it, getting it wrong, or just saying a different name that sounded "close enough".
I hated my name so much that I just didn't use it, and used my nickname instead, even when introducing myself to new people. A typical reaction would be "But what's your real name?", and I was hesistant to say it because I was worried they would laugh (which actually did happen more often than "sometimes").
I eventually grew up, and now I just don't care. People get my name wrong on a daily basis. When I correct them, they feel embarassed and apologize to me, and I just comfort them by saying something along the lines of "It's okay; I'm used to it. People get it wrong all the time". I usually don't even correct them, and let them call me whatever they want. The only situation when I do correct them is when it is necessary for legal reasons.
I need to enunciate my name everytime someone has to write it down in an application or something like that, or I just hand over my ID to let them see how it's spelled because it's just easier that way. I've had a few situations when my name caused major legal problems. You've no idea how much of a mess it can be when your driving license says a different name because someone got it wrong.
As an adult, you may be thinking all I've said is trivial, that giving your daughter a unique name honors her ancestry and it's noble, but this is because you're an adult; you enjoy having your frontal lobe fully developed, and you think rationally. But for most teenagers the severity of their emotional reaction is not in line with the reality of the problem, and she will have to go through adolescence. She will be wondering why her parents, the people who were supposed to love her, gave her a name that is bullying fuel for years. She may hate her name for that, and by proxy, hate you for giving her that name. Teenagers are cruel, and they always find a way to make fun of someone; making fun of someone's name is one of the easiest ways of mocking them.
On top of all of that, you're planning to use a foreign diacritical symbol.
It should be spelled with the i that has two dots above it
You didn't say "Marï"; you just described how the i umlaut (ï) looks.
This is going to be her life. "
Marï, with an
i that has two dots above it". I recommend you at least make her name conform to English ortography.
Let me finish my post with a relevant meme: