What does that mean?
I cannot find what is "verdikleri". Sounds like past tense/gecmis zaman, but the letter "k" confuses me. Third-person plural should be "verdiler".
And what does the letter "i" represent?

Anyone? Thank you

I am not gonna confuse you more, instead, I´ll give you some examples , hopefully you will work it out yourself ;

 Zaman makinesi adını verdikleri bir şey icat etmişler.

[ I heard that] They invented  something which they call it " time machine".

  ad vermek ---> to give a name

 adını vermek ---> to name something, to give a name something, to call something with a name

.............adını verdikleri ----> .....which they call it as "..........."

Kenan adını verdikleri..... >  Something [or somebody] which they call it [him] as "Kenan"

For example ;

Kenan adını verdikleri bir kedi ----> A cat which [who] they call it as "Kenan"

Kenan adını verdikleri bir postacı ---> A postman whom they call  "Kenan"

If we build a complete sentence ;

Bu mektubu Kenan adını verdikleri bir postacı getirdi. ---> A postman who is called Kenan, brought this letter.

A postman - who is called as Kenan- brought this letter.

I appreciate your effort so much! Teşekkürler!