"Iron Maiden" by Iron Maiden off their debut album called "Iron Maiden".

Living in a Box, by Living in a Box from their debut album Living in a Box.

Then there's the band Flowers that released an album called Icehouse, and halfway through the release changed their name to Icehouse - to not be confused with a Scottish band called Flowers - so the early albums are called "Icehouse by Flowers" and the later ones "Flowers by Icehouse".

They Might Be Giants have a self titled track (but not album) included in their third album Flood

Iron Maiden playing the song "Iron Maiden" from yheir album called "Iron Maiden": https://www.youtube.com/watch?v=ufp75XlTp-Q

Slave to the System by Slave to the System on their album Slave to the System.

I thought this was the tackiest shit ever when I was younger, but looking it up now I guess they were a super group so the very on-the-nose-ness of it feels a little bit less bad. I have no idea how I came across the album but I listened to loads of random music.

Electric Wizard by Electric Wizard is easily one of my favorite songs by one of my favorite bands. I especially love when the wizard speaks in this song

Ramones covered R.A.M.O.N.E.S. by Motörhead on their final album, Adios Amigos.

Wilco (the song) appears on Wilco (the album), which is the seventh studio album of Wilco (the band).

Big Country - In A Big Country

ABBA maddeningly released an album called ABBA and an album called ABBA: The Album

green day

motorhead

slip knot

rammstein

canned heat

Big in Japan were not from Japan but they were big in Japan after they released their single "Big in Japan".

Belle and Sebastian had a song called Belle and Sebastian

This one always makes me laugh. Living in a Box on the album "Living in a Box" by the band "Living in a Box"

Angel Witch - Angel Witch - Angel Witch

Seethed has one. It's a b-side that was eventually released on the album "Curiosities, Rarities, and Paraiahs."

I heard one yesterday from the band Hammerfall (I'm sure you can guess the name of the song).

Self-titled albums were a big thing in the sixties, when the record industry was still starting properly. David Bowie's first two albums are both named ‘David Bowie’. With some artists, it's a bit difficult to track all this crap, since vinyls were basically issued whenever anyone was at the factory and not when the artist had a particularly artistic vision.

Weezer had a gag about it, putting out seven albums named ‘Weezer’ over thirty years, the latest one upcoming in a week.

Songs are different, of course, but the reason you see them in classic rock is probably because those dudes are old.

Cloven Hoof, with Album Cloven Hoof and first track Cloven Hoof.

Crash Land - Crash Land is one of my fave songs, which has been in my rotation for quite a long time. Originally one of the remixes made its way into a playlist of mine. When I checked out the original, I was hooked.

Talk Talk

Electric Wizard - Electric Wizard

God's Hate

Shadows of Paradise

This doesn't fit the prompt in a technical sense, but does so thematically:

The band originally known as Imagica changed their name due to overlap with another artist. For one week they went by Nothing and Nowhere (shared with their first album and a track that would appear on a later album) before settling on their current name, The Birthday Massacre. The Birthday Massacre was the original third track of the Nothing and Nowhere LP, but was renamed Happy Birthday during the band's final name change.