Identify the italicized word as gerund or participle. 'wishing' to remain anonymous, he asked the florist to deliver the flowers to the orphanage.

The word wishing is used as a participle in this sentence.
Gerunds and participles look the same - they have the same form of adding the suffix -ing to a verb. However, their function in a sentence is different. Whereas gerunds are used as nouns, participles are either used as adjectives or as adverbs. In this case, wishing is used as an adverb (how did he ask the florist? - wishing to remain anonymous), which is why it is a participle rather than a gerund.