Some firms do use the terms rollover for a rollover and direct rollover for a transfer. I have never received a 1099 where I had to report it on the line 15 a or b (can't think of which it is without looking it up) on the 1040 when the institution did the transaction or when I had the name of the institution as trustee for myself for my IRA ( my name put on the check). I have had to use that line when I have done the rollover myself unless I had the check made out to the bank or credit union I was taking it as trustee for IRA for (my name) . The only "Rollover IRA" with any of my IRA's I had was at Pen Fed for a small one I rolled over myself from Fidelity in the 90's. I did not call to have it changed but when it was added to and combined with another IRA's, there was no problem. They combined several with with other IRA's I had at the time. Mine pensions or 401K's were not called a rollover IRA when I retired or why my husband retired on either of our 401K's or my pension that I cashed out and put into IRA's. On all of ours we had the checks made out to the place we were taking it as trustees for an IRA for (our names). By doing it this way I was able to get the checks through interoffice mail the next day (from 3 states away) and take it to the institution I was moving it to the same day I received the check and did not have to wait for days or weeks like my sister did doing a transfer from a city 40 miles away.
The IRS has this for IRAs from other pension plans. Did you get a 1099 on yours when you had this done? That is the only thing you really have to concern yourself with I think because of the tax consequences if not put on line 15. Retirement Topics - Rollovers of Retirement Plan Distributions