This name is similar to my own name in its fuller form: Y'shayah (in English
Isaiah, meaning G-d’s Salvation). The invocation of the divine is contained in the second ‘i’ in English – the second ‘yod’ in Hebrew, or the second ‘y’ in the transliteration above. As it stands, the name Yasha'na does not specify from where salvation should come.
The suffix ‘na’ provides an imperative emphasis or call for immediate action, in this case ‘delivery’ or ‘salvation’ – because of this, prayer is often inferred in translations, which makes it an indirect reference to G-d. So, the name can be reasonably translated as the urgent request: “Deliver now” or “Deliver, I pray.” But, as you say, the tense isn't perfect because there’s no subject.
You could regard it alternatively, as Ya'Shana or Y'shana, which could mean G-d’s Year or Year of G-d with a little poetic license. Again, it's not a perfect match because the divine reference is usually not given at the head of a word or name.
I hope that helps.