You do not have to request permission to e-mail customers; however, you must provide them with an option to opt-out of receiving your electronic communications, in addition to the other requirements to remain in compliance with the CAN-SPAM Act. Here's an excellent resource for your reference: https://www.ftc.gov/tips-advice/business-center/guidance/can-spam-act-compliance-guide-business

I'm a trademark attorney and have experience advising clients on issues such as this. If the name you're interested in using will be connected to different products and services than the mark registered in Japan, there may be very little risk of confusion. You'll likely have different customers/clients and different marketing regions. Think of the name "Dove." We have "Dove" bar soap and "Dove" chocolate. Same name; however, the products are completely different and are protected in different trademark classes. There is no risk of confusion and the two are able to coexist. One anticipated risk is the mark could ultimately be diluted (i.e. lose its strength and uniqueness), but that depends on a host of other factors. Please let me know if you have additional questions.