Synergy between your social media profiles is certainly important, as it makes your brand memorable. A consistent imagery throughout your profiles make it easier for visitors to familiarise with you. Familitarity encourages liking - customers who had a positive experience with you will be more likely to return; followers will recall your brand when they wish to buy a product that you offer in the future.
That being said, you don't have to use the same imagery across all your social media profiles, but colour consistency is a must. If you check out some of the top brands, you would realise they maintain the same colour profile throughout their social media accounts. Repeat your logo as much as possible too - your logo plays a significant role in branding and should be exposed in as many avenues as possible.
For fashion brands, it can be seen from Cath Kidston, Forever 21, H&M, that they are using their logo across all their profile pictures, and the same (if not similar) cover photos throughout. Even if they do use different imagery, they still maintain a constant colour feel throughout that represents the style of their clothing line.
Hope that helps!