Middle Name Confusion

Hi , Respected there, This is Sekhar from hyderabad , recently i have register with one of the Canada Immigration consultancy. Where they makes a legal agreement with the clients for processing the Visa applications. In which the Service Legal Agreement (SLA) made with Client ( Myself ) in the written format. Where in SLA sheet made on the name of " Somasekhar Raghunath Pilla Pilla ". Actual My Name as per Passport/SSC/Degree and all other ID's issues by State/Central Govt. mentioned as " Somasekhar Pilla" . I never mentioned any where my middle name . I left is blank. As per Passport : 1) Given name = Somasekhar 2) Family Name = Pilla So i am assuming My Full Name will be = Somasekhar Pilla "Raghunath Pilla " is my father's Name . where they mentioned my father's name in middle of my name . So my query is .Canada Immigration Consultancy giving me a reason , that the agreement will be made on " Full Name " . As per their policies full name will be considered as Given Name + Middle Name ( Father Name ) + Family Name. Where i asked to correct my name as per passport which is "Somasekhar Pilla" . they are willing to correct my name and giving the reason that as per Government rules they made the SLA norms and tells that if you want to change the name you will face lot of issues in future . Could you please let me understand what would be the Correct legal name do i need to follow . And how do i prove to my consultancy to correct my name according to the passport ? If my understanding is completely wrong please guide me i will follow accordingly Thanks Sekhar