JR Central announced that starting on July 1st, they are providing additional luggage space called "oversize baggage compartment" on their Tokaido Shinkansen service.
They are located in between the cars, next to the washroom. There is no reservation required to use this space.
Details on the JR Central website (in English)
https://global.jr-central.co.jp/en/info/oversized-baggage/
In addition, the train company continues to provide the space behind the last row of each car as "oversize luggage space" where large suitcases can be stored. Use of this space does require advance reservation, which can be done at the time of booking your tickets.
There is also overhead stowage space, but if the suitcase is too large or heavy it might be difficult to safely store them without someone assisting you.
As a general rule of thumb, it is better to pack light for your travel to Japan, as the infrastructure doesn't always take into account large objects being brought in (Narrow sidewalks, elevators that are tiny, crowded station/concourse etc..)
Visitors with bulky items might want to consider the reliable Takuhaibin delivery service, which can do an overnight delivery for a reasonable fee to most major cities in Japan. Your hotel should be able to help you with arrangements.