I was born

 Yesterday 

I'm from the

 Horse and buggies age 

These

 Days 

Do people

 Even got birth certificates 

Oh

 D'Von

I'm gonna come up with a unique name

 That want frighten the person on the phone who you want a job with 

I'm gonna come up with a unique name

 That want for sure get your resume thrown in the trash 

That you

 Should name your children 

I'm gonna come

 Up with a real unique name in today's world 

Or you have a

 Unique name 

If your name is

 Unique