It is clear that there are some similarities in the way that naming is conducted in these two poems. If we have a look at "Eve Names the Animals," we can see that Eve is greatly annoyed by the way that Adam names the animals, with rather hilarious consequences:
I swear that man
never knew animals. Words
he lined up according to size,
while elephants slipped flat-eyed
hurtled from the underbrush, tusked
and ready for battle.
To Adam, in this poem, words are just blunt tools to be used to do a job as best as possible. Eve's way of naming animals is far more intuitive, as she seeks to find out the essence of the animal and name it accordingly. It is far more of a creative endeavour requiring her intelligence and time, trying to capture exactly the right word for the creature she is trying to name. Note the metaphor that she uses to describe her naming process:
I strung words
by their stems and wore them
as garlands on my long walks.
For Eve, naming is above all something that is creative, a work of art, and a chance to really get to know the animals she is naming.
In "Adam's Task," the overall impression that we get from Adam is that he is enjoying his work, as is shown by the series of completely nonsensical names he picks. Consider the way he moves from "glurd" to "spotted glurd," naming each, having a great time doing so. My personal favourite is the "McFleery's pomma"! The key to this poem, however, lies in the penultimate stanza, where we are told that : "work, half-measuring, half-humming, / would be as serious as play." Although there is obvious humour in this poem, it also suggests that proper work is something that we can do and enjoy at the same time. Adam does take his job of naming the animals seriously, but it doesn't necessary follow that this means he has to do it joylessly.
The similarities therefore are in the way that both Eve and Adam in these two poems take great delight in their task of naming. The difference would be in the way that Eve really tries to capture the identity of the animal in the name that she chooses, whereas Adam is so busy having fun that he picks some ludicrous names.