c. 1400, robous, "waste, broken, or worn-out material," especially "rubble from the demolition of a building, etc.," from Anglo-French rubouses (late 14c.), a word of unknown origin. There are said to be no apparent cognates in Old French; OED says "app. related in some way to rubble."
The spelling with -ish is from late 15c. As "any useless or worthless stuff" by c. 1600. The verb sense of "disparage, criticize harshly" is attested by 1953 in Australian and New Zealand slang. Related: Rubbished; rubbishing.
suffix in pet proper names (such as Johnny, Kitty), first recorded in Scottish c. 1400; according to OED it became frequent in English 15c.-16c. Extension to surnames seems to date from c. 1940. Use with common nouns seems to have begun in Scottish with laddie (1546) and become popular in English due to Burns' poems, but the same formation appears to be represented much earlier in baby and puppy.
<a href="https://www.etymonline.com/word/rubbishy">Etymology of rubbishy by etymonline</a>
Harper, D. (n.d.). Etymology of rubbishy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/rubbishy