Isn't it unconstitutional to name things after a living person, or is that only with regards to putting a living person on the currency?
There's nothing in the Constitution about it. It's just the law.
(E)Prohibition on certain representations.—
No head and shoulders portrait or bust of any person, living or dead, and no portrait of a living person may be included in the design of any quarter dollar under this subsection.
(quarters)
And the "In God We Trust" you see some places is also the law, and for some coins this has a 2-year period after their death they have to wait.
(E)Limitation in series to deceased presidents.—
No coin issued under this subsection may bear the image of a living former or current President, or of any deceased former President during the 2-year period following the date of the death of that President.
(F)Inscription of “in god we trust”.—
The design on the obverse or the reverse shall bear the inscription “In God We Trust”.
(commemorative dollar coins for Presidents)
Also look at this nonsense:
(D)Standards.—
Because it is important that the Nation’s coinage and currency bear dignified designs of which the citizens of the United States can be proud, the Secretary shall not select any frivolous or inappropriate design for any quarter dollar minted under this subsection.
(E)Prohibition on certain representations.—
No head and shoulders portrait or bust of any person, living or dead, and no portrait of a living person may be included in the design of any quarter dollar under this subsection.
(this subsection is about commemorative quarters for D.C. and territories)
(F)Prohibition on certain representations.—
No head and shoulders portrait or bust of any person, living or dead, no portrait of a living person, and no outline or map of a State may be included in the design on the reverse of any quarter dollar under this subsection.
(these are those state quarters you may remember)
(E)Prohibition on certain representations.—
No head and shoulders portrait or bust of any person and no portrait of a living person may be included in the design of any coin issued under this subsection.
(commemorative coins honoring innovators and I do not remember a single one of these)
Anyway this is just one statute about coins. There are all kinds of others about coins and paper currency, and perhaps other similar things.
This doesn't apply to everything, obviously. Where it's prohibited to use an image of a living person, or name something after them, that would be very explicit and specific. For instance, there used to be a prohibition against living people appearing on stamps. This wasn't actually a law, though, it was just a rule of the U.S. Postal Service that they ended in 2011.
One very obvious example of naming something after a living person is when Bill Clinton signed a bill changing the name of Washington National Airport to Ronald Reagan Washington National Airport to honor Ronald Reagan on his 87th birthday. And in fact, a large federal office building had already been named after him, the Ronald Reagan Building and International Trade Center. Reagan is only one of many who has had federal buildings named after him while alive, though.