I wish the FCC was more specific about how to identify the HD streams on radio. The way that the law is written doesn't specify a specific format, or clarify if the "HD" or "HD1" is a legal insert between the call sign and city of license. I've heard the HD or HD1 identified in a lot of different ways/formats.Yes. 47 CFR 73.1201(b)(1) says "A radio station operating in DAB hybrid mode or extended hybrid mode shall identify its digital signal, including any free multicast audio programming streams, in a manner that appropriately alerts its audience to the fact that it is listening to a digital audio broadcast".
So it has to be mentioned, but in whatever way the licensee deems appropriate.
I know a lot of stations that do their legal id wrong. One of WSOC-FM's current ids goes "WSOC-FM in HD Charlotte". "In" is not allowed between the callsign and city of license. WBAV-FM often leaves the "FM" off of their legal id. WBAV-FM never dropped the "FM" from when they had to differentiate from WBAV-AM, and the FM is still part of their legal callsign. The local iHeart and Radio One stations don't mention their HD channels at all, unless we're talking about a subchannel.
I've never heard of a station being cited for just legal ids though. I have heard of the FCC adding it on in addition to other things. I remember maybe 10 years ago reading that a station got cited for the legal id in addition to issues and programs lists, EEO reports and some other stuff.