I often see it without the 's on the maps around the world. Is it grammatically correct to write it without the 's
What we are trying to say here is "The public transport network of Timisoara" / "The Timisoara public transport network". So, we can change "the" to "-'s" in this sentence and it would have the same meaning.
However, it is not uncommon to omit the "the" in titles, street signs, newspaper articles etc in order for it to be read faster. This is perfectly grammatically correct as well.
Therefore, as we said that changing "the Timisoara public transport network" to "Timisoara's public transport network" gives the sentence the same meaning, we can see that omitting "-'s" is grammatically correct as well.
In connected speech or text, it needs to be definite, so it needs either the possessive "Timișoara's public transport network" or the definite article "The Timișoara public transport network".
Titles, captions of diagrams etc, often use "headlinese", omitting articles and some function words; in that context forms like "Timișoara public transport network" are not uncommon.