Matthew and Joe both make great points: it's not unusual and I'll echo that I've had the same experience.
I'd still like to add two things to the discussion.
First, to many, titles telegraph status and responsibility to members inside and outside the organization; it's quite reasonable that you care about it.
The good news is your employer has explicitly said you can use "Lead" in both your working title (with colleagues/email signature) and on your resume (outside the company).
Second, the "bookkeeping purposes" Tymoteusz refers to is also quite normal. Often job titles are standardized across an organization for simplicity and compliance reasons.
If you were concerned about starting at a lower rung, I wouldn't worry about that either. Those who are likely to have the biggest impact on your career advancement are your bosses (and maybe colleagues if you do 360-style reviews). Those people will know what you do.
Of course, this assumes you will also actually do the lead things you want and