is it necessary that perfect participles should start with 'having'?
Participle means a 'verbal adjective.' You have asked a perfectly feasible question. Adding 'having' is just one of the instances of using present participles. So, present participles end in -ing and represent an action as going on or incomplete or imperfect.
Examples of the same are:
We met a worker carrying a sack of coal;
The kid, worrying about the next day's match, couldn't get proper sleep;
My dad, working on his project, slept on the sofa last night.
Banging on the door, he demanded admission.