Should I ask them to change it? Is it a common practice when
negotiating a job offer?
Titles are clearly important to you, so it makes sense to bring it up - just as it makes sense to discuss and clarify any other important aspects of your new job before you accept.
But before you ask the prospective employer to change it, make sure you understand how you intend to react if they don't agree to the change.
If it's terribly important, than express it as a deal-breaker, and be prepared to move on. If you can live with the existing title then ask for the change, but be prepared to accept the existing title.
I've found over the years that overall, titles tend to seem more important to the individual holding them than to prospective employers. A hard-earned "Programmer II" title may be very meaningful to the person who worked their way up from "Programmer I", but conveys little information to the hiring manager in a company which uses a different title structure. Similarly, "Senior Software Engineer" at some companies means that you've been there a while, yet at other companies, it means a distinctly different set of skills and responsibilities than "Software Engineer".
Most (but admittedly not all) hiring managers and recruiters understand this. While there is the inevitable unconscious appeal to hiring someone with current title that exactly matches the title of the position you are trying to fill, most hiring managers can overcome this. Most will look at your resume to see if the tasks and responsibilities you list match the role they are filling - even when the title doesn't match.
Also remember that titles are subject to change, and not under your control. When my small company was acquired by a very large company, everyone's title was changed from "xxx Engineer" to "xxx Analyst" - yet their roles and responsibilities remained the same as before. Oh well.
I know some folks who choose to put a different title on their resume than the one they actually held within a company. In their case, they chose a title that they felt wasn't misleading, but gave the more correct impression of what they actually did (for example, no Developers put down a title of Senior Vice President, or anything like that). It's a bit of a risky move, since if the interviewer determines that the title's don't match, you've got some explaining to do. I don't think it affected them negatively in these case, but I don't actually know for sure.
So ask if they can change the title for you. But be prepared and ready for your next step in case they decide not to do so. You can only know their reaction by asking.