Your question (as well as the previous one) is rather general and considering you’re asking for very very detailed steps without providing any kind of background information or source data you’re essentially asking people to invest a considerable amount of time.

If you can show you’ve already tried to find a solution yourself and then come with specific questions I would expect more people to respond with suggestions.

The FME Academy is a great place to build up your FME experience, both the on-demand training courses, the online live ones or the in-person ones offered by partners all around the world. Or you can just give it a try.

Sure thanks for your support @redgeographics  to make me give out by more providing details.
Please find the scenarios situations snapshot attached here below for the reference for finding the Attribute Road Names or Street Names Gaps in the Shapefile dataset for any specific coverage of area select for the Road Names or Street Names Continuity checks by finding this potential Gaps. 

For this, Road Names or Street Names gaps findings what could be the best logical methods or using FME transformers potentially for this findings. So please help me finding the solution for this problem statement.

Please do refer the screenshot attached for detailed reference. 
Also, please let me if anything is required.

Transformers you may wish to look at are:

• Bufferer + Clipper to Clip out the Road Network at Intersections, leaving behind just the Road Segments between Intersections
• NetworkTopologyCalculator to assign a common subnetwork ID to the clipped roads by which to group together road segments that are end-to-end
• StatisticsCalculator, with a Summarisation Group By NetworkTopologyCalculator _network_id, and output the Histogram summary of Road Names.   The Histogram List can be sorted in descending order of Count/Frequency by ListSorter.  The most frequent/highest count Road Name in each Histogram List is then likely the “right” road name (if use ListSorter this will be the first List item of RoadName.histogram{0}.value, and any other List Item values > List Index 0 in the Histogram of lower frequency of occurence are likely the “wrong” road name”