True Type Font not displaying Correctly
I’ve had this exact same issue with some OTF fonts. In addition, for whatever reason Altium allows importing of vector graphics on the schematic but not the PCB editor (bizarre) which would have made life easier. 

Anyway, my workaround - although far from ideal - was to make the entire logo a single character in a custom font, using the (free) web app Glyphter.


Using Inkscape/Illustrator, type out the whole logo in a new document. 
Export as SVG 1.0
Drag the SVG into an empty cell in Glyphter, and export your custom font. 
Choose that font in Altium and type the character associated with your logo. 


Despite being some legwork to set up, this actually has the advantage of ensuring your logo is 100% perfect and “on brand” every time - no variability in how Altium may track letters, line spacing, etc.