I have seen a bit of resistance in moving to SharePoint Online (SPO) because of a perceived lack of branding tools and the belief that you cannot brand a SPO site to the same degree as an on premise installation. Are these fears warranted, or is SPO ready for your customizations? The short answer is "yes, it’s ready," while the long answer is the seemingly standard, "it depends."
SPO sites can be broken up into two primary categories. Depending on your particular O365 plan, you can create one public facing site per organization and multiple private sites, such as collaboration sites or sites with the publishing infrastructure enabled, for Intranet and Extranet portals. Most importantly for branding, public facing and security controlled SPO sites have all of the branding tools you will find in an on premise installation. These include the design manager, custom master pages, page layouts, display templates, composed looks, access to the theming engine, SharePoint Designer, and more. Thus, the short answer of “yes;" you can create an entirely custom SPO user interface that is branded to match your organization.