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이지현 happens to be a name of a person. What is this 이가 doing between the name and 안되다 ?

normally 가 serves the function of subject marker. What about 이 here after the name and before 가? Is this the same 이 that we use to point to person or thing that are close to the speaker? Typically 가 as a subject marker follows a noun. Is 이 a noun? It really confuses me. It is probably something new to me.

A person's name with 받침 at the end (consonant ending) is sometimes used with "이" as in your setence.

Say there's a person named 홍길동. You can address him or refer to him as 홍길동이.
With "이" after such a name, it seems that you're saying "a person by the name of 홍길동"
like 홍길동이라는 놈, 홍길동이라는 녀석, 홍길동이라는 친구 with a hint of disrespect.

When I was in high school, some male teachers often called a student, say, 홍길동이 when they were not in a happy mood.

The current president of Korea is 이명박. When we talk about politics with friends and criticize him,
we often refer to him as "이명박이" (that guy by the name of 이명박). Again, it has a hint of disrespect.

Now back to your sentence...

또 다른 이지현이 means another 이지현. The person by the name of 이지현 might have done something wrong
and the speaker doesn't want the listener to become like him/her. Notice the speaker doesn't have much respect for 이지현.

You may ask, "Can I drop it?" Of course, you can. Then your sentence will become
"네가 또 다른 이지현이 안되길 바랬던거야." In this case, "이" after 이지현 is simply the subject marker as you know it.

How about a name without a consonant ending such as 김철수?
I think you just have to say it with a slight angry face if I want to suggest disrespect.

thank you very much for your help... a slight disrespect accords to another person by such device, it reminds me of another similar construct but I will open another thread since it's not related to this thread

The phrase itself is pretty strangely constructed. Definitely not a good usage, apart from being "poetic". Perhaps if I see the drama (or is that quote from a novel?), then I would've understood better.