Ikkun...

I am a simple minded person. So i wanna answer : because it is easy on the tounge calling him "ikun" than "hajime-kun"... Ikkun is just ik and kun

Lmao... Just kidding, i just wanna tease u a bit... Teehee~

I think it has to be something about how his name Hajime is written in Kanji. Kanji can have different way of reading, so often Japanese people tend to read the name wrong so they always ask how each of their Kanji is written.
Dunno how his name is written in Kanji but, Hajime can be written the same as the kanji for number 1 (or 1st) (1 stroke line) and number 1 in Japanese is Ichi, so Hana probably did it on purpose calling him I-kun for short and to make it sound more sweetly into Ikkun.
Just my theory though. I could be wrong. But you can check wikipedia for Possible writings for the name Hajime. (Just Google up: "how to write hajime in kanji wikipedia)

If I'm not wrong the kanji used for can br read as Ichigo too

Ikkun’s name Hajime, is written with kanji “一” which means “1”= “ichi”(Japanese for “one”) It’s a common way of making nicknames. Read the kanji the wrong way on purpose for a nickname.
‘ikkun’ is a derivation of’ichi-kun’ shortened. It has a childish nuance so it sounds really like they are childhood friends.
As ‘ichi’ is a more common way of reading the kanji character, it’s possible that Hana misread his name when he was little, though I’m not sure, it could just be on purpose and small kids like to play with sounds of words and names.

I’m a native speaker of Japanese, so I’m pretty confident with my answer.
I hope this helps

ps by the way ‘ichigo’ needs another character for ‘go’.
For example, if you’ve read “Bleach” Ichigo’s name is 一護 (kanji character ‘ichi’ and ‘go’ which means ‘one’ and ‘save’) though this name is very uncommon.
When people hear the word ‘‘ichigi” the first thing people imagine is “strawberry” (苺= ichigo = strawberry)

Also, as well as there are many ways of reading kanji, there are also many ways of putting the sound into kanji.
For example, “Hajime” (はじめ) could be 一, 始, 肇, 甫, 元, 基, 創... etc
The most common kanji for this name are 一 and 肇. (kind of shows how ordinary Ikkun is on the whole)

Lol it doesn't matter, it's nice talking to you (づ￣ ³￣)づ

Thank you very much (˶‾ ⁻ ‾˵)

Japanese is always a mystery to me since there are various ways of reading even for just one word. Your answer explains it though, and I can seem to relate it since I know a little bit Chinese ╮(￣▽￣)╭ thanks so much :3

Guess my theory is about right in spite not knowing much about Japanese :3

You're welcome (^o^)/