What a great question to ask about Orlando! I am not aware of the psychological term of "slighted little brother syndrome," but I do actually think that the issues that Orlando faces as presented at the beginning of the play certainly run deeper than we would first expect. Clearly the central issue of the way in which Oliver prevents Orlando from becoming the young gentleman that Orlando feels he has the right to be is something that Orlando feels very deeply:
For my part, he keeps me rustically at home or, to speak more properly, stays me here at home unkept; for call you that keeping, for a gentleman of my birth, that differs not from the stalling of an ox?
Orlando's comparison of his "keeping" to the "stalling of an ox" clearly serves to emphasise the way in which he has been neglected and abused by his older brother.
However, in spite of the obvious grievances that Orlando has against his elder brother, I also feel, as a younger brother myself, that every younger brother needs to go through a period where they define their own identity away from the rather unhelpful presence of their older brother. Therefore I do think that Orlando's insecurities run deeper, and the play represents partly his process of defining himself away from the rather malignant presence of Oliver. He needs to become a man and the person he wants to be away from Oliver, and at the end of the play, we see the Orlando who has grown up and become a man, because of the way that he has been able to do this. The insecurities of being a younger brother are well-known as you grow up in the shadow of your older siblings, and the play represents the journey that Orlando undergoes to become his own man.