score:4
My advice: either write your surname as MCLARTYJR or forget the suffix altogether. Putting spaces in is asking for IT trouble.
Chinese naming conventions are quite different to western names; aside from not using an alphabet, the (typically) one-syllable family name usually goes before the two-syllable given name; and the two parts of the name are not divisible.
Chinese people, in common with many in East Asia, often use a different name when they are in the west, either romanized by a transliteration convention (which differs for Mandarin vs Cantonese), neither of which precisely represent Chinese pronunciation; or they pick a western name like "John".
As such allowance is given to people who use slightly different spelling of their names compared to official documents.
So MCLARTY or MCLARTYJR will be understood, but if only JR comes out then that is harder to explain.