The short answer is: yes, your flame-resistant (FR) clothing can be customized with logos, name tags, and embroidery.
But the full answer is: it depends!
While there are certainly ways to customize your FR clothing, it's important to do so in a way that does not compromise the flame-resistant properties of the garments.
First, you should ensure that the added elements are not themselves flammable. Stitching and embroidery should be made with flame-resistant thread. Likewise, any printed images should be made with flame-resistant ink silkscreens.
The size of the logo, image, or text is another
consideration. If the garment ever comes into contact with open flames, these customizations should be small enough that they cause minimal damage if they ever catch fire. A good rule of thumb is that they should be no larger than a credit card.
(Find out How to Select Flame-Resistant Rainwear)
Ultimately, it is the employer's responsibility to determine whether these additions are permissible. But so long as the alternations are minimal and there is some effort to use flame-resistant materials, customizing FR clothing certainly an option.