Travelers Information System radio stations are licensed under Part 90 of the FCC rules. (90.242)
A quick reading of that part shows no requirement for a legal ID as AM stations licensed under part 73 have. It could be somewhere else in the rules that I did not see.
In some services, like transmitter-to-studio data links used for remote control telemetry on AM or FM stations, the ID can be done using morse code which may not be heard easily under NOAA or any other programming.
I am not familiar with TIS rules enough to say exactly what is required. Literature from the major TIS equipment manufacturers does not say anything about ID's either. I was asked to research these systems by our company several years ago. They can only be operated by government type agencies. Cannot be used commercially and saying anthing specific about commercial establishments is limited.