Basically, my officemate is teaching a course this semester on 'The Punic Mediterranean', and I'm having to stop myself from making bad jokes about it, which has led to my wondering whether Punics actually had any concept of puns or wordplay in the first place. Did they, or am I putting the Cathage before horseplay?
With respect to Carthage in particular, Thonemann's (2016) introduction to Hellenistic coinage suggests that the Carthaginians made use of a somewhat roundabout visual play on words on their money. A connection is often drawn between minting and the payment of mercenaries or (especially under the Romans) professional troops, and it's commonly accepted that states would often mint coins specifically for paying mercenaries. This is especially true of Carthage, which minted coins on the Sicilian shekel, the Attic tetradrachm and the Corinthian stater weight-standards, presumably to cover all the various origins of their hired hands (though the latter two became more standardised by the fourth century BC, with the stater weighing three Attic drachmae.)
In particular, coins struck on the Greek weight-standards, which are the most likely candidates for paying foreign (i.e. Greek) mercenaries, could often include an image of a palm tree, which was a motif that was also common in bronze coins intended for local circulation. To just rattle off a list of examples (you can view more at wildwinds), there's:
This mid-late 4th century BC gold stater, with a palm tree on the reverse,
This late 4th century BC gold stater, also with a palm tree on the reverse,
In particular, the lattermost issue, on the tetradrachm standard, appears most likely to be one of those employed for mercenary payments due to its use of the Greek goddess Persephone, as opposed to the Punic goddess Tanit, who was more common on domestic bronze issues. Thonemann in particular cites ANS 1967.152.696 and ANS 1944.100.79789, both Siculo-Punic tetradrachms from around the turn of the third century, as arch-examples of a sort of 'bilingual' coinage, employing both Greek and Carthaginian imagery that would be interpreted either way by whoever was viewing it. In the former example, the image of Tanit, with contemporary Greek hairstyle and surrounded by dolphins, also evoked the Greek nymph Arethusa, while in the latter example the divinity is instead Heracles, evoking the coinage of Alexander. And on the reverse side is a horse with a palm tree.
All this talk of palm trees. What does it all mean? Well, the Greek for 'date tree' or 'palm tree' was φοῖνιξ (phoînix). And the Greek for 'Phoenician' was Φοῖνῐξ (Phoînix). Basically, it's plausible – though of course not necessarily definite – that the Carthaginians were conscious and made use of the happy coincidence of Greek homophones and their own civic symbols.