i know this is a joke but I'm going to use your hypothetical question to expound on the history of rap.

Today we use the terms "rap" and "hip-hop" interchangeably, but in its earliest days the music was termed "hip-hop," with rapping as one of the components of hip-hop, done by the MC. The other component was the DJ. Hip-hop, in its earliest conception, saw the DJ as the primary focus of hip-hop - the MC served mostly a secondary and functional purpose. Hip-hop was being played at block parties, birthday parties, the MC really was the "Master of Ceremonies" in the truest sense - they were mostly there to make announcements, announce the next party, etc. They'd do this over the DJs beat though, and there was often some wordplay involved - Grandmaster Caz notes a typical announcement

You know next week we gonna be at the PAL where we rock well, and we want to see your face in the place

So you can see some wordplay going on, but its clearly not "rapping." Due to the influence of Jamaica on rap, it could be considered similar to Jamaican "toasting."

The first "rapper" as we understand rap today was Cowboy, who performed with Grandmaster Flash (and the Furious Five, but this is before the Furious Five). The raps though were extremely simple stuff like

throw your hands in the air and wave them around like you just don't care

I said a hip hop, hippie to the hippie, the hip, hip a hop, and you don't stop

yeah that second one comes from the Sugarhill Gang but most MCs were using some variation of it. The "raps" were not super original nor intricate at all, and they weren't going for verses. I mean hip-hop was really party music, meant for performances at block parties and the like, and the MC at this point is really only there to get the crowd pumped up - the most important part of hip-hop is still the DJ, who is actually creating the music people are dancing to.

As the Sugarhill Gang song show though, by 1979 though rappers were going for verses, and were rising in importance in hip-hop. Here's a good example of early hip-hop. But the rhymes were still extremely simple. Sugarhill Gang in 1979 go:

See I am Wonder Mike and I'd like to say "hello"

One year later in 1980 Kurtis Blow goes

I'm Kurtis Blow and I want you to know that these are the breaks

Saying your name and then something that rhymes with it was common because it was so simple and also a good way to get your name out there. What better advertising is there than just saying your name over and over. So this is probably the origin of "my name is x and I'd like to say." Someone somewhere probably said that because at the time it would'nt've sounded dated/cringe, but was very in line with what everyone else was saying on the mic.

This of course sounds corny to us because this rhyme style is extremely extremely dated. It's a stereotypical rap line, but from a time when rap was very very young. Even that early hip-hop I linked above - Kool Moe Dee classifies the early flow styles into two periods: 1973-1978, and then in 1978 Melle Mel (who performed with Grandmaster Flash) transformed rhyme cadence, which was the dominant style until 1986 (this style is still I should say very old school - 1986 is the year I think most people would recognize a more modern form of rap, a product of Rakim's technique). So even some of the stuff I put in here as "simple raps" but that came after 1978, doesn't really capture just how simple rap was in that early early old school period, 1973-1978.

So “I’m x and I’m here to say” is not really a white thing, but just a really simple rhyme that harkens back to an earlier period in hip-hop's history.

tldr: Coke la Rock and Kool Herc are the utopian socialists; Cowboy and Grandmaster Flash are Marx and Engels; Melle Mel is Lenin; Rakim is Stalin; Biggie Smalls is Mao. “I’m x and I’m here to say” is the equivalent of quoting the utopian socialists - important thought in the development of socialism/rap, but we've moved far far past it at this point.

The other reply is amazing, but also Barney Rubble used it when he stole Fred Flintstone's Fruity Pebbles in 1988. I think this cultural memory still has a major impact today.

Yeah pretty much but sometimes people are just leaning into it