An infinite number. A polygon with any number of sides can be equilateral (ie have sides of equal length).
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A rhombus has 4 sides of equal lengths
None but it has end sides of equal lengths
An isosceles triangle has 3 sides and 2 of its sides are equal in lengths
There are infinitely many 2d shapes. They can have 1 side (a circle or ellipse) to infinitely many. They can have sides that are straight or not, the sides can be equal or unequal in length, the angles can be equal or unequal, etc.
There are many such shapes and there is no specific name.