Its Tricky one... but as per international or geographical logic, you are always refer to your passport name correct, means SNIP or Federal will not be bother to see Aadhar Card, they are more concern on your passport as this is the only document you will travel. So, you trying to say that name on your passport is correct and Aadhar card carries wrong name, but why your bank is so much concerned on Aadhar card? its always advisable to get your correct name on the experience letter, let them understand that they should mention the name which is appearing on passport as the visa will be based on the passport details and not Aadhar card, i am unsure how flexible your employee is but the way they are behaving seems they are not kind enough to help you.
See Sandeep, i am seeing your case as visa officer ok, so i know you already had a problem with your documentation where you can not provide me substantial proof of experience, now this is another problem where the name is differ... i know its a small difference but yes difference is there,,, so what i am trying to say that you need to minimize the explanation to visa officer for each document... you know what i mean, like i understand one exceptional issue, than you come up another issue with the name so it will only raise questions,
Try your best to get the experience letter based on the passport, otherwise you need to attach the evidence why your employee is not ready to provie you the experience certificate as per your passport, you might provide the Aadhar card as proof but again you need a very solid proof to link that Aadhar card & passport mismatch... and if you will provide both passport and aadhar card there is abig chance that officer will raise his eyebrows and might think that ..ok now which name is real correct name? so to close that doubts or loophole you should be providing your birth certificate, degree certificate etc.
My question, why can't you change your Aadhar card name?
Thanks.