Your strategy should encompass at least four components:

(A) Complete Visual/verbal/social/technical audit to find/create needed assets for transition: know which assets need to be retired or replaced and what transitional assets are needed to bridge the gap. Prioritize: not everything always needs to change at once and the more you have the longer it will take or cost. Plan to convert brand book concepts/guidelines into tangible or digital deployables: how much "stuff" do you need?; vendor selection; budgeting; designing production files; ordering; quality assurance etc...

(B) Internal (team) awareness & asset deployment program and monitoring compliance.

(C) External publicity plan: aimed at existing clients & prospects, and any other stakeholders: social networks, media, affiliate partners, etc... Timing should be coordinated with industry / sector calendar (trade shows, if applicable), and major app update for maximum effectiveness. Do you need specialized short term PR/AD help? How can you leverage your 10K+ users to buy in / get the word out?

(D) Technical migration & Monitoring Plan: seo strategy & tracking including all affected url redirects, landing pages, email changes, whatever is affected. Monitoring & analytics to see how effective the transition is (compared to old name stats) and when transitional assets can be retired.