'pet-welcoming' is a modern English compound formed from 'pet' + 'welcoming'. 'Pet' (modern English) refers to a domesticated animal kept for companionship, and 'welcoming' is the present participle/ adjective form of 'welcome'.

'pet' entered English in the late 16th century (Scots/English) as a word for a tame or indulged animal or a beloved child; 'welcome' comes from Old English 'wilcuma' (wil- 'desire' + cuma 'guest'), which became Middle English 'welcome' and later the adjective/participle 'welcoming'. The compound 'pet-welcoming' is a recent coinage modeled on compounds like 'pet-friendly' (20th–21st century).

The original components kept their basic senses ('pet' = a favored animal, 'welcome' = received gladly); combined, they now specifically describe places, services, or policies that accept or are accommodating to pets.