It is usually called an intersection or an intersection point.
Intersection
If they do intersect, it will be at their point of intersection.
point
No, two straight lines can intersect at only one point and that is their point of intersection.
Two lines that intersect at a right angle are called perpendicular.
Lines that intersect to form right angles at their point of intersection have slopes that are negative reciprocals.
intersection
Point of intersection
When two lines intersect at a right angle, they are "perpendicular"
Theorem: If two lines intersect, then exactly one plane contains both lines. So, when two or more lines intersect at one point, they lie exactly in the same plane. When two or more lines intersect at one point, their point of intersection satisfies all equations of those lines. In other words, the equations of these lines have the same solution, which is the point of intersection.
It is the point of intersection.