Both 〜と呼ぶ and 〜という can be translated as “to call...”.
So, for situations where something is given a name, what's the difference between the two?
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～と呼ぶ is used to tell someone to call you by a certain name or term.
For example, Joseph Joestar's famous phrase from JoJo's Bizarre Adventure is:
Which translates to:
"[My name is] Joseph Joestar; call (address) me [as] Jojo."
It's used to tell others to call you by something you specify.
I am Momotaro; call me Momo.
Nice to meet you, I'm [called] Aria - call me Ari.
This example has both the "iimasu" form, which is used to introduce yourself, and the "yobe" to tell people to call you by the name "Ari".
"言う" is used for introduction, and it's not formal either - don't forget to use the masu form with it - while "呼べ" is used to tell people to address you by a certain name.
That's the use of "呼べ" in your question and not in general. Its meaning is "to call".
For example, 「モモを呼べ」 means "Call Momo!".