3 WP installations on the same domain, with the same header

Here are a few stategies you might try depending on your situation.

You could create a theme with a custom header and apply that theme to all three sites.

If you needed each site to have its own theme, you could also create a minimal parent theme with basically just the header and make three other themes that inherit from that parent.

If your themes are already set, you could do the same thing with a plugin. You’d have the plugin create the header and style it. Most likely, it would have to either be absolutely/fixed positioned, or you’d include a little JavaScript to position the element wherever you want it on the page.