Can you use the medical symbol Rx in a business name? For instance, if you have an R in your business name, can you legally cross the bottom part of the R to form the medical symbol?
But then it’s not a letter* and at that point I think it would become a logo. As far as logos are concerned, as long as your not stealing someone else’s, I’m not sure there are too many rules.
*OTOH, it would probably just be considered an ‘R’ for the purposes of reading it.
Registering a business name: The rules vary from place to place but are generally that you are restricted to using only the alphabet/writing system of the country where you want to register. For somewhere like the USA that might be letters from the basic Roman alphabet plus the typical punctuation marks, plus numerals. As you can see, this would not include the Rx prescription symbol. The rules for your specific location should be easy to google.
Registering a trademark: You are not prevented from using any symbol or design or string of characters, etc. that you care to use, except for those that are in contravention of your local trademark policy/laws. In this case, I can imaging that it is possible that a trademark for something including the prescription symbol Rx might be objected to if it were not for an actual medical or pharmaceutical practice.