Is the negative potential of 書く used in this sentence and what is its meaning?

Question

I am reading a manga and a girl is showing her tutor that she "started her test." All she has is her name written down. Here is the sentence. お前しか書けてないがいいぞ. I believe the tutor has said this. The preceding sentence was said by the girl and was　私もう始めてます。

I can't quite pick up on what is being said here. It seems like 書けてない is the negative potential form of 書く. So my obviously wrong translation is, "Not being able to only write your name is good." This makes no sense. I'm just taking every word at face value so to speak. If anyone could provide a proper meaning for this sentence, I would greatly appreciate it.

Answer 1

I think it's:

名前しか書けてないがいいぞ。

しか...ない means "no(thing)...but" → "only". (not "not...only")

書けてない is a contracted pronunciation of 書けていない. ～ていない can mean "have not done (yet)". (See: Why is a verb in the past (た形) contradicted with ～ていない? ) ～しか書けていない here literally means "have not been able to write anything but~~" "(have) managed to write only~~".

The が means "but". (It's a conjunctive particle, not the subject case particle.)

So the whole sentence means:

"You've only written your name, but it's good."