What is the name of this plant?
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That is a thistle, though which variety is hard to tell until it blooms.
However. In many locales it is illegal to allow thistle to grow. And if you let that thistle go to seed, next year you may discover why. It will be everywhere and it's a very hardy plant. It will survive your lawn mower by staying low instead of growing upward.
Thistles are wonderful plants in the right circumstances, they can hold soil in place very well to inhibit erosion on hillsides, and they are an amazing bee plant in rural areas, but you really do not want these growing in a residential neighborhood.once they've taken hold in a general area they are very hard to get rid of because if you miss but a single plant, then thousands of seeds will blow in the wind and spread them all over again for your next year's joy.