Process is an intransitive verb, but it means "walk in procession". Clergy and ministers process into a church service. It's pronounced differently, with the stress on the second syllable.
ODO doesn't allow process not to have an object, in the sense which is meant in your quote:
verb
[with object]
perform a series of mechanical or chemical operations on (something) in order to change or preserve it:
the salmon is quickly processed after harvest to preserve the flavour
* deal with (someone or something) using an official procedure:
the immigration authorities who processed him
* Computing operate on (data) by means of a program.
However, it is also fairly common for computer output messages to omit the verb, headline-style; or to use jargon.
In the quoted message, it is clear what is meant: the request went through the process. But this use is jargon.
Best Answer
Yes, you definitely can. These are instances of reduced passive relative clauses. Reduced relative clauses are common in English:
Sometimes, as the Wikipedia article shows, reduced relative clauses can be too ambiguous. But your examples do not have that sort of ambiguity. Merged is the past participle of the verb to merge, which is used in the passive voice.
Thus, instead of saying
you can drop the bold part and you get the phrase you suggested: