I want to get my boyfriend a ring that has the letters "AS" engraved because they are the letters in his name but I was reading that AS is a term of respect used for prophets. If I got the ring with those letters would it be disrespectful to wear?
Using abbreviations like AS or PBUH or SAWS etc. is considered by many scholars (almost all Sunni scholars) as lazy and inappropriate as we are required to fully praise our prophet ():
Indeed, Allah confers blessing upon the Prophet, and His angels [ask Him to do so]. O you who have believed, ask [ Allah to confer] blessing upon him and ask [ Allah to grant him] peace. (33:56)
Some scholars concluded from this order of Allah
... that (writing it in abbreviated form) does not serve that purpose and is devoid of the virtue of writing “salla Allaahu ‘alayhi wa salaam (May Allaah send blessings and peace upon him)” infull. Moreover the reader may not take notice of it and may not understand what is meant by it. It should also be noted that the symbol used for it is regarded as disapproved by the scholars, who warned against it. (Source islamqa #47976)
So for a Muslim it is not recommended to use an abbreviation instead of fully sending prayers and blessings to our prophet () and therefore there's nothing exclusive in using any such abbreviation as the abbreviation itself is hardly legitimate.
Further more in Islam a relationship between unmarried people of different gender is basically haram if there's no mahram relationship between both.
No, it is not. And it is not considered a good practice and it is disapproved by many scholars and even few scholars have considered it as haram as it does not serve the purpose and there is no evidence of using it by companion and Ahle-Ilm.