I received a full scholarship to do a PhD in the US. The immigration specialist asked me to send mine and my fiancee's details to send the I-20 forms for the both of us. I have received them now and in my fiancee's it says that the relationship to me is "spouse" although we are not yet married but will be about a month before leaving to the US. Will this create a problem during the visa (F1,F2) interviews as the date of marriage comes after the date of issue of the I-20 of my fiancee. Please help me out. Thanks!
Although there was a misunderstanding, you may be fortunate since you intend to marry before you leave for the US. However, as it will take place after the visa interviews, her visa could be delayed until you provide the evidence of the marriage. Without that, her visa status may be at risk (as might yours), as she is not eligible for an F-2 visa until you formalize the union. Nonimmigrant dependent family visas are not is given to those not married, whether they be engaged or domestic partners.
There are other methods: the partner either arranges for their own US sponsorship, through a university or employer, or applies for a B-2 tourist visa as a cohabitating partner (added emphasis and paragraph breaks for readability mine):
9 FAM 402.2-4(B)(5) (U) Cohabitating Partners, Extended Family Members, and Other Household Members not Eligible for Derivative Status (CT:VISA-193; 09-28-2016)
(U) The B-2 classification is appropriate for aliens who are members of the household of another alien in long-term nonimmigrant status, but who are not eligible for derivative status under that alien's visa classification. This is also an appropriate classification for aliens who are members of the household of a U.S. citizen who normally lives and works overseas, but is returning to the United States for a temporary time period. Such aliens include, but are not limited to the following: cohabitating partners or elderly parents of temporary workers, students, diplomats posted to the United States, and accompanying parent(s) of minor F-1 child-student.
B-2 classification may also be accorded to a spouse or child who qualifies for derivative status (other than derivative A or G status) but for whom it may be inconvenient or impossible to apply for the proper H-4, L-2, F-2, or other derivative visa, provided that the derivative individual intends to maintain a residence outside the United States and otherwise meets the B visa eligibility requirements.
If such individuals plan to stay in the United States for more than six months, they should be advised to ask DHS for a one-year stay at the time they apply for admission. If needed, they may thereafter apply for extensions of stay, in increments of up to six months, for the duration of the principal alien's nonimmigrant status in the United States. You should consider annotating to indicate the purpose and length of stay in such cases.
You did not indicate when you intend to go for the visa interview so may have to adjust this answer. Check out this very helpful FAQ in regards to F2 Visa
The final question in the article speaks directly to your situation.
I'm Engaged. Do I need to be married to receive a dependent I-20/DS-2019?
It is acceptable to go through the process to add a dependent spouse to your SEVIS record before you actually marry. However, you must be married and have the marriage certificate in hand by the time you apply for the dependent visa, or for Canadian citizens, when you enter the U.S.
So you have to be married and take the marriage proof with you to the interview. Since you mentioned you will be married only a month before you depart. That would be cutting too close for the interview I would say. Earlier the better generally.
My personal opinion on an alternative would be to do the court marriage atleast, that way you are married and can take the marriage proof along. But ensure to have the pictures etc with your spouse and family.