I'll start off by saying, one of the most lucrative periods in my career was working under such an arrangement. At that employer, I had access to consistent long term clients that would have been hard or impossible to get on my own. They were willing to pay top dollar, too. I was partially involved in the sales process, so I knew how my work was priced and I had a vote in how contracts were put together. It was great. However, I've seen many other people (even some of my coworkers at that same employer) terribly unhappy with this sort of pay structure.
You asked a few questions.
Is it a good scheme?
Depends - "good" is subjective and is dependent on which party is defining good and what they're hoping to get out of the arrangement. This type of scheme can have advantages for both the employer and the employee, though. The thought behind schemes like this is to incent the employee to be useful to the client, because being useful would hopefully mean the client is willing to pay more per hour and also willing to sign up for more/longer projects. It motivates the employee to apply themselves, work hard, and make sure there's a good relationship with the client.
The employer is happy, because they have motivated staff who are doing their best to be useful and valuable. They're also happy because they have a fixed relationship between income and expense - they don't have to worry about smoothing out periods where they have a lot of people on the bench (because they're not paying you as much, or at all) versus periods where everyone is busy.
There can be disadvantages, too. As a consultant, you ultimately might not have a lot of direct control over your salary in such an arrangement. If other people are selling the service, officially managing the client relationship, setting the contract terms, and so on, then you're basically at their mercy in terms of what your paycheck is. If someone in charge of sales decides to sell you at a really low rate just to close a strategic deal, you may find yourself "underpaid" while working on that contract.
So - before switching to such an arrangement, it's useful to make sure you understand the process of selecting and negotiating contract terms. For instance, if you have a title of "Senior Consultant" does that mean you're always quoted and billed at $X rate? Or do the salespeople decide what the contract rate is on a case by case basis? I'd definitely want to understand that before signing up.
Is there a name for this kind of setup and is it common?
I've heard it called many things, I don't think it's incredibly common but it's also not exactly uncommon. It seems to be more common, in my experience, in smaller consulting firms where bench time (having consultants not billable) is hard to manage. A larger firm with lots of depth can "even out" busy and less busy times and may be less likely to offer such a program.
Could I make 100% of that profit working alone?
None of us can answer that. You might make nothing working alone. Or twice that. It's important to consider that your employer is providing some kind of value for the 25-35% they're taking off the top - administrative functions, sales, and so on. If you work for yourself, you have to do that work too, and it's often not billable.
And on that note - a scheme that's paying you 75% of the billable rate equates to a 1.33x markup, which is incredibly low. In other words, most employers mark up more than that (they keep more of the money for themselves).
If you're comparing this deal to working on your own as an independent contractor, (your "can I make 100% working alone?) then you need to consider the value the middleman (your employer) is able to add to the contract. If this sort of scheme gets you access to clients you couldn't get to on your own, it can be a very good deal. For instance, government contracts requiring extensive overhead or boilerplate. Or contracts that are incented towards women- or minority-owned contractors (common in the US in certain industries). Or, simply, if your employer is keeping you busy without you having to do unpaid work: sales, admin, or other overhead, this can keep you focused on actually earning money. You also need to consider your risk aversion, because - obviously - there's risk in any scheme where your income is variable.
And if you're comparing this to the flat salary deal at this employer, you really need to understand how contracts are priced and how work is assigned among your fellow employees. If you can work hard, show off your skills, and end up being billed on lots of high dollar projects, that's great. But if someone else is pricing your rate arbitrarily, you may find yourself unhappy with your income. And if your employer can't keep a steady pipeline of clients, you may find yourself making lots of money when there's lots of work, and little money other times when there's no work to do.