There is no specific name. It is one of the medians, angle bisectors and perpendicular bisectors: one set of these is coincident and is the line of symmetry.
An isosceles triangle has 1 vertical line of symmetry
ohcourse an isosceles triangle has a line symmetry
An Isosceles triangle has at least one line of symmetry but if it has more than one line of symmetry it can be an Equilateral triangle as well as a Isosceles Triangle. So a triangle with one line of symmetry is always Isosceles and If it has more than one it is always an Equilateral triangle as well as an Isosceles triangle. Example of an Isosceles triangle:
An isosceles triangle has only 1 line of symmetry.
An isosceles triangle has 1 line of symmetry
An isosceles triangle
An isosceles triangle has 1 line of symmetry
An isosceles triangle has two equal sides and one line of symmetry
An isosceles triangle
An isosceles triangle
an isosceles has only 1 line of symmetry
An isosceles triangle has 1 line of symmetry, an equilateral triangle has 3 and a scalene triangle has no lines of symmetry.