Okay so I am coming up with ideas for a potential story. I am naming my strong female protagonist and I looked up some character names. I like the old german last name Stark, it fits with my character and it means strong and brave. The problem is, i'm afraid if I give her this last name people will think of Tony Stark, aka Iron Man. What should I do? I really like the name...
My first thought wasn't even Ironman but Game of Thrones "Stark". Either way, you are going to have people with common last names. We have the last name "Smith" pop up 1000 times in movies and stories, but in this case it is so common of a name that there really is no hard associations outside of maybe Agent Smith from The Matrix.
If you don't want them to be mixed up with another universe/story then you should probably not pick a last name that is already heavily associated to someone else.
Try to see if there are variations of the name such as spelling or different names with the same meaning. Ultimately, you will need to choose between an already popular last name or spending more time finding a strong unique name.
Seeing how "Stark" is a widely well-known name because of Game of Thrones and Ironman, I would advise against it because even if people won't criticize you for it (but they probably will), it will still feel you're riding on the popularity of those other books if yours is in the same genre.
Basically, it'll just seem fanfic-ish and unprofessional. There will be people who will most likely think to themselves, "Ugh. This person named their character Stark. How unoriginal. They probably did it because they like Game of Thrones."
Again, you are allowed to use the name "Stark". It's not prohibited by law. People have similar names, and you can't really copyright them.
In conclusion, there's probably no harm in it if you're not writing your book in the same genre as those popular ones who already use the name "Stark", but if you are, I would definitely advise you try to change the whole name or just the spelling to avoid peeving your readers.
Go for it.
I honestly don't see any problems with that. "Stark" is a very common name, nobody would raise an eybrow. A proof of this, is that every time I read/watch Game of Thrones, I never think about Iron Man, and when I read/watch Iron Man, I never think about GoT. Stark is a common name and a very neutral one: it's not so specific or meaningful.
It would be different if the name was Targaryen, or Baggins, or even Tolkien or Shakespeare: in this case it would be necessary to have a reason to use something that would totally look like a citation, a reference. Which is done in many successful cases: Umberto Eco's The name of the rose's main character is named Guglielmo da Baskerville as a direct reference to Sherlock Holmes: that is intended, and adds up to the novel's world. A guy who just happens to be named "Rufus Shakespeare" would just sound odd.
Other than that, I wouldn't worry. Nobody owns names (unless they are brands, of course) so you won't risk anything.
Trying to create a truly unique name is often fraught with danger. Especially if you're writing in an existing/established world (such as ours), or one that is heavily influenced by it (such as GoT, for example).
The problem isn't with the name itself, it's with the character (unless it's a truly unique name). Stark by itself will not draw connotations with Iron Man. Unless your character is a genius, billionaire, playboy(girl) philanthropist. Likewise, it won't draw connotations to Game of Thrones unless they are Northern Lords, adhering to a strict code of honour and have a propensity for losing their heads.
However, sticking with period/setting appropriate names is perfectly acceptable. Any work set in the highlands of Scotland during the wars for Independence, for example, would expect a plethora of McDonalds, Campbell, William, Bruce, MacTavish etc.
That said, I'd advise against following the likes of Christopher Paolini with Eragon. If it's a cookie-cutter fantasy world, try not to blatantly steal the names of established characters that have obviously heavily influenced the writing.
Stark is a common family name and names are not copyrighted. As mentioned above, if she comes close to exibiting character traits, like Tony Stark/Iron Man, than be weary. Otherwise, use your name.
In fact, if she has a nerdy friend, you're safe to draw some parallels to the two as long as it's clear to the others that she's distinct. For example, if she is a massive technophile BUT is a high schooler and super hero tropes are not present in the work (beyond acknowledging real life fiction) than that's perfectly safe for said friend to from time to time call her "Tony" because of the association (because it's just at the tip of my mind, the TV series Heroes got away with one character nicknaming a Japanese character (with prominant cheeks no less) "Pikachu" which is a much more distinct name than Stark in fiction. In Happy Days, there were frequent jokes centered around character Ralph Mouth having parents named Mickey and Minnie. And from my own personal work, the I once wrote a character named Mickey who I characterized as shorter than other kids his age and sort of mischievous, earning him the nickname "Mouse" from some of his friends. These are all allusions to their much more famous namesakes and can be used to inform the audience to keep an eye out for characteristics that can be associated with your character. As long as the character stays distinct enough so that it is clear you're only making the association in the form of nicknames or puns for laughs, there is little you need to worry about.
I will say, that, with the personal example that I provided, copyright issues related to "Mouse" did prevent me from moving forward from the project at large, but it wasn't to do with Disney. Rather, Mickey was one among many characters that were someone else's idea but had lapsed into the public domain. My problem was I was interested in international distribution and I didn't want to publish in countries where different copyright laws exposed me to possible action from copyrights related to the characters still extant in that nation. But that's a horse of a different color to what you are asking, I'm just being fair.
TR;DR: It's safe to use the name. It's safe even if she has traits that create loose, nickname like associations with other fictional characters (i.e. loves her technology or loves table top gaming of the fantasy genre). This stuff will fly, but just keep clear of flying to close to the sun with it.