Here are some pun-based name ideas combining "monk," "Jackie Chan," and "pun," aiming for a variety of tones:

Humorous/Silly:

• Monk-ey Business (referencing Jackie Chan's action-comedy style)
• Chan-do the Pun-ishment (playing on Chan's name and the idea of punishment)
• The Shaolin Pun-isher (combining martial arts and puns)
• Jackie's Pun-derful Monastery (a playful take on a monastery setting)
• Pun-Fu Master (combining martial arts and puns)
• Zen and the Art of Pun-Maintenance (a humorous take on Zen Buddhism)

Clever/Witty:

• Chan's Pun-derdome (a clever play on words, referencing a fighting arena)
• The Illuminated Pun (referencing enlightenment in Buddhism)
• The Kung Fu Punster (combining martial arts and puns)
• The Meditative Punsmith (combining meditation and puns)
• The Silent Pun (a paradoxical and clever name)

More Abstract/Conceptual:

• The Way of the Pun (referencing the Buddhist path)
• The Pun-damentals of Chan (a play on fundamentals and Chan's name)
• The Enlightened Pun (referencing enlightenment and puns)

Names incorporating all three elements more directly (may be less catchy):

• Jackie Chan's Monk Punnery
• Monk Jackie's Pun Emporium
• The Pun-ishing Monk (Jackie Chan style)

The best choice will depend on the specific context and desired effect. Consider the target audience and the overall branding when making your final selection.