wait your spoiler is kind of wrong (like its worded in a way that's misleading)
She remembers the first time she and hideto meet and how she misread his name as "eito". The 'ei' part sounds the same as the letter A and she proposed to write it as A. I can't read spanish so I made do by checking with multiple translators/dictionaries online. Because of that I don't actually understand why she decided to do that even though it's wrong (mispronounciation) but from the multiple sources I tried to run the words through it might have been because both of their names have numbers in it (mitsu is 3, eito is the pronounciation of 8 in english) but yeah it doesn't make sense why she would pick A then.
Yes she makes up with her boyfriend in the end, but not because his name also starts with an A it's because the 'A' that she originally wrote on that paper was some kind of code/nickname for her boyfriend in the first place.
Spoiler
She end up with her boyfriend because his name also start with 'A', She find out in the end.
And
If anyone wants to see raw u can see here
https://tmofans.com/library/manga/22592/A--Answer