I just had a rebuilt engine put in and when I start it usually when it's cold I get this constant ticking noise until I start to accelerate. Once I had been driving and engine warms up it stops. Can anyone tell me what the ticking noise is. Thank you

 

Most likely it is a lifter. Cold oil is thicker oil. When the engine warms up, oil thins and flows better. Hydraulic Lifters use oil pressure a part of their function. A ticking lifter can be a weak lifter. Assuming the lifters are new in the rebuilt engine, I have bought sets with the occasional weak lifter. There is also the possibility the rocker arm wasn't tightened properly, but that is usually a tick that won't go away. If the lifter gets weak enough, it won't let the valve open far or long enough affecting engine performance. There is also the possibility the oil pump is weak, but again, we assume such to be new/refurbished in a properly rebuilt engine.
BTW... welcome to the forum! When you need an issue addressed, it helps if you inform others as to the year and engine size, mileage, maintenance etc... You get the idea. More info is good info right?