Had to use Google Translate and the meaning is still unclear. Please speak in English so that we Tunisians can understand the problem properly.

I remind that Arabic is read from right to left, and I see some confusion in the explanation.
So let’s explain it:
The first part of the name (you described it as the second) is شبيكة (Chbiket).
The second part of the name (you described it as the first is الجريد (Ejjrid).
So we get: شبيكة الجريد
Tunisian Arabic, the name you should be referring to: Chbiket Ejjrid
Modern Standard Arabic literal romanisation: Shabikat Al-Jarid/Shubaykat Al-Jarid.

So, the second word does have the Al- definite noun prefix, Al-.
The first word is already feminine. -a, it does have the ta marbouta (Shabika/Shubayka).
I don't understand the third remark.

So, it is correct: شبيكة الجريد.
Please romanise it as "Chbiket Ejjrid", because this is the name we say in Tunisia.
Nevertheless, thank you for your remark. Resolving the note.