Does the style (if it is) shown in the picture below have a particular name?
English Language & Usage Stack Exchange is a question and answer site for linguists, etymologists, and serious English language enthusiasts. It only takes a minute to sign up.Sign up to join this community
This shorthand is known as textspeak.
SMS language or textese (also known as txt-speak, txtese, chatspeak, txt, txtspk, txtk, txto, texting language, txt lingo, SMSish, txtslang,or txt talk) is a term for the abbreviations and slang most commonly used due to the necessary brevity of mobile phone text messaging, in particular the widespread SMS (Short Message Service) communication protocol.
At one time, back before there was any even arguably good reason for it, this was called Princespeak.