I'm modelling an activity diagram for a project. Directly after initial node is it okay to use a decision node. I just google for it. But I fail to find similar examples even. Eg:- imagine a person can Search for a dog name or Select the category animal, then dog likewise at the very beginning.......
One of my team mates mention that according to above example those are two different activities and we should create two activity diagrams for it.
Your team mate isn't wrong. This is a design question which should have been clarified beforehand. Activities are functional parts inside of use cases. They represent scenarios like "sunny day", various error scenarios, etc. And again one step back the use cases represent the added value the system under consideration represents for its primary actor.
Now from your examples it's hard to tell what that system should be. Search for dog name could be a use case, but in which context? Is it to name a new dog or to search for an existing dog in a database? Same for Select animal category(and then dog?). Both do not make much sense as use cases. Once you come up with meaningful use cases you can tell exactly which steps the activities should have as actions. Only then you can have the need to decide. The decision which use case to actually use it outside the system and you wont see the steps done for it.
As a recommendation: Bittner/Spence have an excellent book about use cases which (unlike the UML specification) makes a lot of sense. There are also other well known authors teaching the same school (along Ivar Jacobson).