There is no restriction, as long as it is rendered either as TeX or with the logo, and as long as the reference is to the actual TeX(-related) software.

That said, it is not likely that any lawyers will be sent after you; however, beware of peer pressure, which can be considerable.

At the time of the attempted registration, I actually handled the letter from the Honeywell lawyers, asking that DEK and AMS cease and desist from use of the name. This is a case where peer pressure did have a strong effect, since Honeywell was then a computer manufacturer, and DEK was already a leading light of computer science. A compromise was worked out by which the TeX form of the name was agreed to be acceptable, if used consistently.

There has not been a later attempt to register the trademark; however, Knuth's standing internationally is sufficient that if the name were "misused", there would probably be at least a few reasonably local interested persons to object. In fact, this is what we count on when complaining about PDF copies of The TeXbook found on the web; in most parts of the world, this is sufficient to get them removed.

Totally unrelated to TeX, but it might be of interest to note that the supermarket group Carrefour ^[1] holds various trademark registries for the name "TeX" and multiple logos, some of which closely resemble the TeX logo:

In most countries, this trademark is registered ^[2] for textile (not texlive as I was about to write) products such as shirts, pants, sheets, underwear, baby clothes, etc. But in France at least, the list is quite longer, including for example scientific devices, games, medical devices, lighting/warming/cooling devices, security devices (for cars, bikes, etc.), jewelry, printing devices, leather, furniture, cleaning and cooking devices, toys, etc.

This should not prevent from publishing books about TeX and LaTeX, but it might be a problem if we wanted to sell a TeX (or TeX.SX) t-shirt for example.