Should the PhD supervisor's name be first in a scientific journal? I am a self funded PhD student and have been told by my supervisor that her name should be first on any future journal I will be publishing during my studies under her supervision as "this is the only thing she gets from her PhD students".

I am just wondering if the ordering of author names matter? She is going to help me only by proof writing my article. All research will be done by myself. 

Is she legally allowed to say it? Should I accept it?
I am just wondering if the ordering of author names matter?


In a small number of academic fields -- like mathematics -- the overwhelmingly majority of jointly authored papers list the authors' names in alphabetical order.  In these fields, a non-alphabetical ordering of the authors stands out like a sore thumb: the average mathematician knows it is meant to look bad for the latter-listed author but is not sure exactly what it means.  In a field like this, if you hear a potential advisor say this, you should say "Thank you, I'll look for someone else" and walk out the door.

In most other academic fields, the ordering of the authors conveys important meaning in a manner which can be subtle and vary from field to field.  There are some academic fields where being the last named author carries a lot of prestige, but in my understanding this is the kind of prestige awarded a very senior person.  I don't know of any academic field in which putting the junior author at the end looks good for them.

But anyway, here is another kind of answer to your question: the ordering of names must matter to your potential advisor or she wouldn't have brought it up!  Therefore if you yourself are not sure what rights you are signing away in such an agreement, you should be especially skeptical.  I think the first thing that you should do is look around to see how common this practice is among other faculty and students in your department.  (If you are in an academic context far from the American one, it would be more prudent to do this even if you are in a field like mathematics than to immediately walk out of the office like I suggested above.  I don't know what the standard arrangement is at every math department in the world...obviously.)  This will be easy to check just by looking at the publications of the faculty members.  Also asking the other students can help. 


  She is going to help me only by proof writing my article. All research will be done by myself. 


Proofreading is not the same as advising.  An agreement where your advisor guarantees in advance not to advise you in most meaningful ways and that she will insist on first coauthorship sounds like an especially bad one.  It also sounds unethical to me by the general standards of academic ethics, although subfield ethics may have a role to play.


  Is she legally allowed to say it?


Not every form of bad behavior is illegal (thank goodness).  I can't speak to the law over the entire surface of the earth, but in the US there are certainly no laws pertaining to this kind of thing.


  Should I accept it?


I think that what potential advisor is really trying to say is that she does not want to be your potential advisor.  Sometimes people have trouble saying "no" outright; this happens in academia (where the tenure process takes a good shot at making "yes-men" and "yes-women" out of academics) but also in life generally.  A lot of times I have seen academics offer to do things for students only under quite unreasonable conditions that they clearly (to me) expect the students to turn down...only to have the student not know so clearly that the conditions are unreasonable and accept them.  Of course both parties end up unhappy.

In your case I feel reasonably confident that your advisor is trying to tell you to go away.  What I am unsure of is whether she's telling it to you specifically or to all students generally: the rather oafish "this is the only thing she gets from her PhD students" seems to indicate that this professor is simply not onboard with the practice of having PhD students at all.  But either way, I advise you to look around: probably you can do better.