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Recently I've seen this slogan.
Its spelling and pronunciation are a bit unusual:
"Nice to meat you" means "it's nice to provide you with some meat dish",
but it sounds like "It's nice to meet you" as if you are introduced to somebody.
My question is: How can we name this linguistic phenomenon?
Your slogan is an example of the pun.
According to Wikipedia (https://en.wikipedia.org/wiki/Pun):
The pun, also called paronomasia, is a form of word play that exploits multiple meanings of a term, or of similar-sounding words, for an intended humorous or rhetorical effect.
These ambiguities can arise from the intentional use of homophonic, homographic, metonymic, or figurative language.
In your case there is a homophonic pun, which uses homophones MEAT and MEET.
