Can you give us a photo of a single blade, so we can see the variegation more clearly?

There are a couple of Carex morrowii, including 'Ice Dance' and 'Ice Ballet' which have green center blades with white margins. The variegation in 'Ice Ballet' is the more distinct of the two, but 'Ice Dance' is a more established cultivar.

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That looks like a Lirope to me, not a grass. A variegated kind. Does it get purple blooms? Donn is much better than me at this but thats what I think it is.

I don't know lol... i didnt pay attention last year, sorry.. right now its got like tiny plumes in light color

Woops. I just read the last part of your post. I think I had this on the brain because of another lirope question and am newly assessing the stuff invading into my yard from next door and am feeling a bit lirope-phobic right now. Never mind. Ha!

I'm almost certain it's a Sedge, but beyond that, things get fuzzy.

As has been noted, there are so many Carex varieties, and there has been so little done to categorize them completely, ID is difficult at best.

I don't think it's one of the popular C. morrowii cultivars like 'Ice Dance' or 'Ice Ballet.' The variegation just isn't vivid enough. It may be C. morrowii 'variegata,' but even that has more apparent variegation. There are green-only versions of C. morrowii, and this may be a blend between that and C.m.'variegata.' It could also be a sport of another Carex like C. flacca, C. nigra, C. sylvatica or C. pensylvanica.

If you really want to chase it down, we need more photos and more information. A closeup of the bloom would be a big help. Does it produce offsets, and if so, where do they occur in relation to the mother plant?

A note: It looks like you trimmed it at the wrong time; too late in its growing cycle. The slightly slanted ends on the blades indicate it was trimmed after the new growth had begun. The trimmed blades continued to grow in length, but show the trimming at their ends.