Sure, there are a couple of ways a gift can be structured. An
endowment is a perpetual fund that gets invested by University money managers and a portion of the annual dividend/interest is distributed for the named cause each year. The current minimum is $50,000 to start one and it can come from one person or group of people who raise it and it can be increased over time. I believe they distribute about 5-7% a year and skim a percentage to fund the fundraising call center. So a $50k fund would distribute about $2500-3500 annually to the named cause. This keeps the fund healthy in down market years and lets it still grow a little over time in step with inflation. There are many named scholarships that distribute smaller amounts like this. To fully fund something like a coach or professor position, you would need a lot more capital. Generically, UC Davis has an endowment of $1.66 billion held by the UC Davis Foundation, but this is made up of hundreds of funds, some very specific and some general.
The alternative to an endowment gift is a
current use fund gift. This is spent in its entirety the year it is given and could be one-time or recurring. For example, if you want to give $2500 every year, but don't have the $50k for an endowed fund, you sign an agreement to give $2500 per year for x number of years and the award ends when you stop giving. Again they skim a percentage, so you actually have to give like $2750 for the recipient to get $2500.
There are also a few capital funds for specific projects, like there's one to fundraise for Baseball batting tunnels.
If you go to
give.ucdavis.edu and search "athletics," you will get a long list of funds you could donate to, some endowed and some current use. They don't advertise how much is in any one fund. I don't know how forthcoming Athletics would be if you asked, but I know on other funds the University is coy about their investment details.
One thing to keep in mind is that there is always fine print saying that your gift is irrevocable and the chancellor can redirect to other uses without your permission if they see fit. Not common, but happens. For example, there was an Aggie Band endowment that was pretty clear in that it could only be spent on a student-run band and if such a band ceased to exist, the alumni band would direct its use. When the Band-uh got burned down, the university stole the endowment funds for unintended uses and said the chancellor could unilaterally do whatever he wanted without recourse. After much fighting, the University made a "one time exception" to allow donors to redirect their donation to a different endowment but categorically refused refunds. Again, this is not a common situation, but I was insulted enough that I cut off donating to any endowment funds. If it concerns you that some chancellor in 20 years might co-opt your gift for something you disagree with and you have significant funds, you would need to form a private foundation to carry out your wishes. The University hates that idea by the way, since it takes control away from them.