Good question. I haven’t come across much in the way of recent branding assets that include the wordmark. All I know is that openhistoricalmap.org features this SVG image of the OSM logo with an “H” inside the magnifying glass. It displays that logo with “OpenHistoricalMap” in the site’s default font, which is the system’s sans-serif font. If the page uses plain text instead of an image, it can similarly match the system font.
At some point, we should consider designing a more distinctive logo for OHM. The present logo is very similar to OSM’s, which is useful but also not as imaginative as it could be. Maybe we could start by discussing (in a separate thread) what we want out of a logo before putting out a call for proposals. Your design sense would be helpful for that effort.
Anyhow, the main thing left for this page redesign is to get rid of the spaces. @jeffmeyer has registered the “OpenHistoricalMap” trademark with the USPTO on behalf of this project, so it’s important to use it consistently. For all I know, it might also cover “Open Historical Map”, but I think that spelling is too close to the unrelated “Open History Map” project for comfort.