I don't think putting it on or near the handle is a good idea. Not all braille readers read at the same speed, and I would hate to be in the way of someone trying to get through the door while I'm trying to read the braille. Door handles are also at a really bad height for ergonomic reading for us taller blind folks. I also don't want my hand or wrist to be broken if someone from the other side opens the door quickly. There is just too much that can go wrong with this idea.

Braille signage should be at an average height on a wall adjacent to the door, where we can stand out of the way of the door traffic and also not get hit by the door when trying to read. If it's a quick short name, that might be ok for the handle, but as others have said, unless I know it's going to be therein the first place, I'd never think to hunt for it. I recommend trying something else altogether for this project.

This is one of those catch-22 situations: it's not helpful unless it is the norm, and it's not the norm because it's not helpful if it's not the norm. If every door had braille signs, this would be a massive help especially in the work environment and for things like sports facilities, schools etc. However, the fact it isn't the norm leads to one very clear drawback: blind people don't think to look for them. If it was normal for door signs to be in braille, in a standardised place and this was known about, it would make my life easier.

Another potential drawback is that a lot of blind people are functionally illiterate. In an age of school cutbacks, lots of people simply don't end up learning braille and have to rely on electronics. I'm lucky that I ended up learning it, but every year a smaller percentage of people are.

Depending on where you are, they may already be laws/rules regarding placement of braille signage.

In Ontario, we have the Canadian Standards Association’s “Accessible Design for the Built Environment” (https://www.csagroup.org/wp-content/uploads/B651-18EN.pdf) which specifies where the braille sign should be.

4.5.6.4 Location of tactile signs
A tactile sign
a) if used to identify a door, be mounted on the wall beside the latch edge of the door;
b) where applicable, have the leading vertical edge 150 ± 10 mm from the door jamb (see Figure 11);
c) where double-leaf doors are used or no wall space adjoins the door’s latch edge, be mounted on the nearest adjacent wall;
d) allow a person to approach the sign to within 100 mm without encountering protruding objects or standing within a door swing;
e) be mounted with the horizontal centreline 1500 ± 25 mm from the floor; and
f) have a clear wall area around the sign at least 75 mm wide.

I should point out, though, that I've been to many buildings (and even government buildings) that don't conform to the code.

So my college did this, we had plaques on the left side of the doors saying the room numbers.

Would definitely be useful if it were a standard, but the usual problem applies of how to find the signing if you don't already know it's there. The notion isn't bad though.

Even people who are illiterate in braille might be able to tell the difference between pull and push. The two final letters being the same helps already. Then again, this is coming from a fluent braille reader so maybe not.

Another possibility would be providing a braille sign and also a relief of the letters in print, that might be more recognisable to people who lost their sight later in life and have not learned braille yet, or ever. Something like the relief in licence plates is very easy to touch-read.

Hell yeah that would be helpful!
Especially in businesses and shopping centers.
Right now, I just kind of barge into businesses and ask what they do if I’m in an unfamiliar place. It would be very helpful to have signs in braille on doors.