What are different type of training required for a Software Requirement Engineer?
The correct answer is, it depends. Software requirements training should fit with the type of project management used by your organization.
One type of training you don't need
Many people think a software requirements engineer should thoroughly understand programming and software engineering. Obviously, you should know something about the software engineering discipline, but knowing too much can destroy your ability to write good requirements. This happens for two reasons.
First, good requirements should ignore the technology (such as which platform or language is used). This is because requirements should not dictate the solution; they should only define the problem to be solved. Devoting too much study to the technology will bias a requirements analyst toward particular solutions. This makes consideration of alternate solutions more difficult for the design engineers.
Second, requirements elicitation is an art as much as a discipline. Managing stakeholders, conducting meetings, choosing elicitation methods, and choosing methods for representing information require strong skills in psychology and communication. Putting all your energy into learning programming languages and tricks will cost you on the human side. It would be as great a mistake as putting all your energy into market research. You need to know enough about programming to win the respect of the designers and to communicate with them, but your job is to build a bridge between the customer and the designer.
What should I wear? Well... where are you going?
Organizations that work with large systems that integrate multiple technologies tend to follow traditional Project Management and Systems Engineering methods. They use some variation of the Waterfall model, such as the V model.
For a high-level understanding of Systems Engineering requirements methods, I recommend starting with INCOSE's (International Council on Systems Engineering) Systems Engineering Body of Knowledge (SEBOK) and using the SEBOK as a guide to subjects for study. Also consider studying Model-Based Systems Engineering, one subset of traditional methods, and SysML, the modeling language used for MBSE.
Organizations that work primarily with software tend to follow Agile project management methods. In Agile environments, requirements engineers tend to go by the title Business Analyst. I recommend starting with the IIBA's (International Institute for Business Analysis) Business Analysis Body of Knowledge (BABOK) and using the BABOK as a guide to subjects for study.
Agile is a set of principles and not an actual method. I have asked for a recommendation for a book that describes the different methods (such as Scrum and Kanban) but have been told no such book exists; for each Agile method, you need to find a different book.
The requirements methods differ considerably between traditional and Agile. Traditional methods nail down requirements and then negotiate schedule and cost. Agile nails down schedule and cost and then negotiates, prioritizes, re-prioritizes, and drops requirements.
The two methods do share some of the same tools. I suggest studying Unified Modeling Language (UML). UML is not a language, but a set of graphical methods for defining requirements. The most commonly recommended book on software requirements is Software Requirements, 3rd edition, by Karl E Wiegers and Joy Beatty.