I would call it trochaic tetrameter with alternating feminine and masculine rhymes. Even though it a fairly common meter, I don't know a better name for it.
If you leave out the last syllable of a trochaic line of poetry, it's called a catalectic line. So if all the lines of your poem had trochaic feet with the last foot reduced to one syllable, this would be called catalectic trochaic tetrameter.
But saying trochaic tetrameter with catalectic alternate lines is much too cumbersome a phrase, whereas alternating feminine and masculine rhymes is easier to understand (if not shorter).
A feminine ending of a line of iambic poetry ends on an unstressed syllable, while a masculine ending ends on a stressed syllable. It is fairly common to alternate feminine and masculine endings in English poetry. Another example of this meter is Housman's poem Reveillé, which begins:
Wake: the silver dusk returning
Up the beach of darkness brims,
And the ship of sunrise burning
Strands upon the eastern rims.
Wake: the vaulted shadow shatters,
Trampled to the floor it spanned,
And the tent of night in tatters
Straws the sky-pavilioned land.
There are also poems where only the lines with masculine endings rhyme. You can describe these by the phrase "with alternating feminine and masculine endings." A good example of these is Maya Angelou's poem Equality, containing the following stanza:
Take the blinders from your vision,
take the padding from your ears,
and confess you've heard me crying,
and admit you've seen my tears.