Are there recommendations to use "Hubble-Lemaître constant" instead of "Hubble constant"? The IAU recommends renaming the Hubble law as the Hubble-Lemaître law, as discussed at its General Assembly in 2018 (see this press release and the links therein).

I have now stumbled upon an occurrence of "Hubble-Lemaître constant". Are there any recommendations (or noteworthy statements, opinion papers) in favor or against this extended interpretation of the IAU resolution B4 to the terminology for $H_0$?
No, only the Hubble law was recommended to have its name changed (I'm a member of the IAU, so hopefully I'd have known if there were more votings).

However, several astronomers (including myself) found the voting a bit… weird; while acknowledging the work of George Lemaître is admirable, many more people than him and Edwin Hubble contributed to the understanding that the Universe is expanding. So, some were joking that we should rename the Law to the Slipher-Friedmann-Wirtz-Lundmark-Lemaître-Robertson-Hubble-de Sitter-Humason law, or something like that.

Others joked that if the Hubble law should be renamed, we should also start referring to "the Hubble-Lemaître Space Telescope", "the Hubble-Lemaître Ultra Deep Field", "the Hubble-Lemaître Bubble", and, as you have seen, "the Hubble-Lemaître constant". Others probably also did this non-jokingly.

Btw., astronomer Virginia Trimble wrote a paper six years ago (Trimble 2013), arguing that we should name the Law after anybody but Hubble…