Rebranding a business while maintaining search engine rankings is a delicate balancing act. If executed incorrectly, it can result in loss of organic traffic, customer confusion, and decline in brand reputation. However, with careful planning, you can minimize the risks. 

Here’s a step-by-step guide to rebranding without losing search ranking:

1.Research and Planning:

• Identify the Scope: Determine what is changing: just the domain, or brand name, logo, content, or all of these? 
• Audit your Current SEO: Understand your current rankings, backlinks, most visited pages, etc. This will give you a baseline to measure against after rebranding.

2.Choose a New Domain Carefully (if changing):

• Make sure the domain hasn’t been penalized by Google in the past. 
• Consider a domain name that’s relevant to your business and easy for users to remember.

3.Maintain Content Quality:

• If you’re re-writing content, ensure that it maintains (or improves upon) the quality of the original content. 
• Keep the URLs similar if possible, as URL changes can affect ranking.

4.301 Redirects:

Implement 301 redirects from your old pages to the new ones. This tells search engines that the old page has permanently moved to a new location. It also transfers about 90-99% of the ranking power to the redirected page.

5.Update Backlinks:

• Reach out to websites linking to your old domain and request them to update their links to point to your new domain. 
• Use tools like Moz, Ahrefs, or SEMrush to identify your most valuable backlinks.

6.Update Google Search Console & Bing Webmaster Tools:

• Add and verify your new domain. 
• Submit a change of address in Google Search Console. 
• Resubmit your sitemap.

7.Update Google Analytics:

Adjust the domain settings, and ensure you’re tracking the new domain correctly.

8.Maintain Social Media Presence:

• Announce your rebranding ahead of time and frequently. This prepares your audience and reduces confusion. 
• Update social media profiles with the new brand name, logo, and any other branding elements.

9.Monitor Rankings and Traffic:

• Closely monitor your search rankings and website traffic after the rebranding. This helps in identifying any issues early on.
• Use tools like Google Analytics, Google Search Console, and third-party SEO tools to keep an eye on traffic, search queries, and rankings.

10.Engage in Branding Efforts:

Enhance your branding efforts to push the new brand name. This includes PR campaigns, content marketing, social media marketing, and even offline marketing.

11.Feedback & Adjust:

• Continuously gather feedback from your users/customers about the new brand. 
• Be ready to make adjustments based on feedback and any issues that might arise.

12.Review On-page SEO:

• Ensure that on-page elements like title tags, meta descriptions, and headers are relevant and optimized for your new brand. 
• Remember, communication is key during a rebranding phase. Your audience, partners, and stakeholders should be well-informed about the change to minimize confusion and to ensure a smooth transition.