Lovejoy coupling have the number on the back for type and size if replacing existing coupling, for example L050 type 0.500" size shaft.
If new setup you can measure the shaft with a dial caliper or look up the specs as given on the name plate of the pump. For the motor side look up the frame number and it will give you the shaft size. you can purchase couplings online at many outlets if you do not have a local supplier.
COMMON
SPECIFICATIONS U.S. Metric
Bore 0.787" 20 mm
Standard Liquid Temperature 160°F 71°C
Above 130°F call Cat Pumps for inlet conditions and elastomer recommendations.
Crankcase Capacity 18 oz. 0.55 l
Inlet Ports (2) 1/2" NPT(F) 1/2" NPT(F)
Discharge Ports (2) 3/8" NPT(F) 3/8" NPT(F) Shaft Diameter 0.787" 20 mm
Weight 19.8 lbs. 9 kg
Dimensions 11.73 x 10.0 x 5.24" 298 x 254 x 133 mm