competitor claiming "official site"

Hello


One of my client's competitors is claiming to be the "official site" in a google AD , taking traffic from my client .

Should I file a DMCA claim? , contact google ads? trademark the name?

basically the competitor has the name of my client which is an artist painter and wrote next to his name "official online gallery" .

for example in the google ad is says "John Doe | Official online gallery"

Thanks