Last Name different in I797 and Passport

[PJohnson]

Last Name different in I797 and Passport.

My Husband changed his last name while we married in Sanfrancisco Court. With the marriage certificate as a proof for his name change he got his SSN name changed to new name. He got his indian passport also fixed. Now the question is we are planning to go for H1 B stamping to Canada (We are Indian Citizens). Will this be an issue when we go for H1 stamping in vancouver. We both are FTE working for big companies in the silicon valley. He has a US degree as well. He had his first stamping in Vancouver. This would be his second.

Can you please tell me if he will have any issues since he has different last name in I797 and his passport.