Here are my suggestions on how to approach the US expansion:

Launch the brands separately with distinct websites and social media accounts. This avoids confusion for US consumers who are unfamiliar with your Hong Kong brand umbrella approach. Selling such distinct products—skincare and hair loss treatments—together may seem disjointed or less focused to new customers.

Prioritize bringing your core skincare line first since that business is more established. Use a different brand name that can be trademarked in the US. Build an independent presence and equity in that market for the skincare line before introducing the hair care line.

Once the skincare line gains some traction, you can launch the hair care line independently under its own trademarkable brand. Cross-promote between the two brands since you own both. This allows you to build awareness for both distinctly first before linking them as sister brands.

Maintain separate websites and social channels for now. As both gain equity in the US, you can then transition to a master brand website that hosts or links to the two sub-brands. But launch separately first so US customers get familiar with each independently based on their own merits.

Navigating the expansion of your skincare and hair care businesses to the U.S. involves careful considerations. Here are insights to address your concerns:

Q1: Launching Under Same Website and Social Media

Pros:
Cost Efficiency: Managing a single website and social media account can be cost-effective.
Cross-Promotion: Leverage existing customer base for cross-promotion.
Cons:
Brand Confusion: Consumers might find it confusing to see both skincare and hair care under one brand.
Target Audience: Tailoring marketing messages becomes challenging when catering to two distinct audiences.
Recommendation:

If maintaining the same website and social media account, clearly segment content. Design your website to have distinct sections for skincare and hair care. Use social media stories or highlights for clear product differentiation.
Q2: Positioning in the U.S. Market

Pros:
Test Simultaneously: Gauge consumer response to both skincare and hair care products.
Diverse Audience: Attract a broader audience interested in both categories.
Cons:
Resource Allocation: Requires substantial logistics, ad spend, and website management for both brands.
Market Feedback: Simultaneous launch might make it challenging to identify which category resonates better.
Recommendation:

Launch both categories but start with a soft launch. Monitor analytics to understand consumer preferences. Gradually refine your strategy based on market response.
Q3: Considerations for Decision-Making

Market Research: Understand the U.S. market demand for skincare and hair care. Identify competitors and consumer preferences.
Brand Identity: If maintaining a single brand, ensure clear messaging that communicates diversity in product offerings.
Logistics: Evaluate the impact on logistics, shipping costs, and inventory management for dual product lines.
Digital Marketing: Plan targeted digital marketing strategies for each category to avoid consumer confusion.
Adaptability: Stay adaptable and be prepared to pivot your strategy based on real-time market feedback.
Final Thoughts:
Consider a phased approach based on initial market responses. Leverage customer feedback to optimise your strategy over time. Seek legal advice on trademark challenges and explore creative solutions to maintain brand integrity.