I was named from a very popular song. Everyone sang it at me. To make matters worse, both my first and middle names are foreign in honour of family heritage when I was born and raised in the UK. Even some family members openly said they disliked me having a foreign name.
Of course it got shortened, and over time evolved into a different name, one that can be a standalone name. When I started secondary I asked to be known as my nickname because the Victorias got to be Vickys and so on, but the teachers said no as it was too different to my real name. I was heartbroken. But my friends called me my nickname and variants of it. My DM told me about deed poll, but also that I could go by my middle name if I wanted (like my DGM did) but I got shit about that too, although there was an A lister at the top of her game at the time with the same name, or just choose a nickname to go by. I went with option 3. As I got older I just introduced myself as my nickname. Now I use my full name professionally and my nickname everywhere else. It means my colleagues rarely find me on social media and some of my friends don't even realise my full name.
My DS has changed his name a few times. He started primary under his nickname. By the time he was year 3 he opted to use his full name. When his DF fucked off he opted to use my surname. I never pushed any of this. I actually told him to wait until he went to secondary school and have it as his known as name, but next thing I know I got a call from his teacher saying he'd gone to the office and asked to use his Mum's name please. I said yes of course if that's what he wanted, so they changed it over that day. His secondary school have mucked up a few times and used his Dad's name, but he says "That's my birth name, please call me [my name]".
Today he came home from school and said he'd quite like to change his first name to one of his nicknames when he deed polls his surname. I said that's fine, it would be his choice, but to bear in mind he can use any name he likes as long as he uses his official name when necessary. Pointed out all the people in our lives who use nicknames without issue, and suggested he'd get many more nicknames over the years as he's only 12. He then reeled off all the names his friends have given him and realised it would be hard to choose, so maybe he'd stick to his full name and have lots of nicknames. I said "fine, but you've got at least 5.5 years to make your mind up, and you dont have to change it at 18, so just experiment!" The nickname he suggested to change to is one I use and love on him, so it's no problem for me and it definitely sounds cooler than his full name, but it's not necessary to deed poll it.
Not quite the same scenario, but as my DM was relaxed about my identity crisis I decided to go the same way. Thinking about it, I first wanted to be known by this name at 11, it was well established by 16, with some teachers capitulating and using it, and I'm now 37 and still happy to be known by it. It can be a phase, but it may not be. Best thing to do is give facts and support in a neutral way so she feels confident to make her own choices.