I rolled my old Roth 401k into my current Roth 401k. The 1099-R lists the tax code as H, which I see is for rollovers to Roth IRAs. Is this going to cause any issues?

I have two concerns:

1) Is the tax code of H correct even though the rollover was to another Roth 401k, not a Roth IRA?
2) The 1099-R lists me as the recipient, even though the checks were made payable to the firm managing my 401k plan. Is that going to cause any issues that may make it look as though I took a distribution?