Yes! We can name it as \(\vec {OB}\) as \(\vec {OA}\)  and \(\vec {OB}\) represent the same ray. We cannot write the ray \(\vec {OA}\) as ray \(\vec {AO}\) because the starting point of ray \(\vec {OA}\) is O whereas the starting point of ray \(\vec {AO}\) is A.
Five rays have been drawn below:

(i) AB and CD, BC and AD,
(ii) \(\angle A\ and\ \angle B,\angle B\ and\ \angle C,\angle C\ and\ \angle D,\angle D\ and\ \angle A\)

(a) In the given figure, point O is the centre of the circle.
(b) Three radii of circle in the given figure are OA, OB and OC.
(c) Here, OA and OC are radii such that OA and OC are in a line. So, AC is the diameter i.e. diameter = 2 X radius.
(d) In the given figure, ED is a chord of circle.
(e) Points P and O are in the interior of circle.
(f) Point Q is in the exterior of circle.
(g) A region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides is called a sector. In given figure, OAB is a sector.
(h) A region in the interior of a circle enclosed by a chord and an arc is called a segment of the circle. In given figure, region enclosed by ED is a segment.

\(\triangle EFB,\triangle AFB,\triangle DBC,\triangle FBC,\triangle ADE,\triangle ADB,\triangle DFE,\triangle AEB,\triangle AFD.\)

(a) We know that, a triangle is a three sided polygon. So, three triangles in the given figure are as follow:
(i)\(\triangle ABD\) (ii) \(\triangle ADC\) (iii) \(\triangle ABC\)
(b) An angle is made up of two rays starting from a common end point, here the names of seven angles are as follow:
(i) \(\angle BAD\) (ii) \(\angle BAC\) (iii) \(\angle CAD\) (iv) \(\angle ABD\) (v) \(\angle ACD\) (vi) \(\angle ADC\) (vii) \(\angle ADB\)
(c) The names of six line segments are as follow:
(i) AB (ii) BD (iii) DC (iv) CA (v) AD (vi) BC
(d) From the given figure, it is clear that \(\angle B\) is common of \(\triangle ABD\ and \triangle ABC\).

(a) The diagram is shown as below:
Here, \(\angle ROQ\ and\angle QOP\) have one point O In common.

(b) The diagram is shown as below:

Here,\(\angle MON\ and \angle ONR\)  have two points O and N in common.
(c) Drawing a diagram of two angles, such that they have three points in common, is not possible.
(d) Drawing a diagram of two angles, such that they have four points in common, is not possible.
(e) In the figure given below, \(\angle SOT\ and\angle POT\)  have one ray \(\vec {OT}\) in common.

(a) The following figure shows a closed curve, but not a polygon, because a polygon is made by line segments only.

(b) The following figure shows an open curve made up entirely of line segments.

(c) It is not possible, because a polygon of two sides cannot be drawn.

A rough figure in each of the cases is given below:
(a) Point P lies on \(\bar {AB}\).

(b)\(\overleftrightarrow {XY}\) and \(\overleftrightarrow {PO}\) intersect at M.

(c) Line I contains E and F but not D.

(d) \(\overleftrightarrow {OP}\) and \(\overleftrightarrow {OQ}\) meet at O.

\(\angle A\ or\angle DAB,\angle B\ or\angle ABC,\angle C\ or\angle BCD,\angle D\ or\angle CDA\)