I have these 2 shrubs (circled in red) that I need to trim.
I'm wondering if I can turn them into/trim it into a spiral shape (like in the 2nd photo).
I'm finding it very difficult to find what kind of shrubs I have and if it's possible to do this.
In one word, no, sorry! Training an evergreen by practicing topiary starts when the plant is small and involves repeated prunings over a few years. If you took your existing evergreens and pruned them into spiral shapes you would expose inside areas of the plant where there is no growth.
Most evergreens do not bud or grow from old wood with the exception of yews. This means after you pruned the areas showing the trunk would not grow out. You can see this when people find their cedar hedge getting too tall and they cut off all growth over a certain height. It looks powerfully ugly for a few years but the new growth from the perimeter grows up to cover the cut branches.
In your case new growth is only going to come from the perimeter of the shrub which will not give you the look of trained shrub.
Topiary demands yearly or twice yearly attention to keep the plant in shape. Perhaps you would be better off to plant a trained evergreen as they are commonly available at many nurseries in the States and Canada.
Edit: ItsMatt asks about an arborist that will prune your evergreen into a shape reminiscent of the cloud shape referred to here. You can do this too if you have a healthy evergreen but this is not the same look as the topiary spiral the original question referred to. It won't kill a healthy evergreen but older shrubs will still take yearly pruning to maintain a nice shape.
