Getting regular check-ups is vital. but I would put seeing a dietician as not that important. Blood tests can only tell you so much and depending on your health insurance they can either be expensive or the doctor could be reluctant to order it. Plus dieticians may come out of your own pocket.
For vegans, you should assume you are deficient in Vitamin D, and Omega 3s (and there is no blood test for omega 3). If you are a female you probably should make the same assumption with calcium and iron.
Checking your nutrient intake with a tool like SparkPeople and Cronometer can tell you a lot more. the only caveat is that absorption of nutrients varies.
B12 is a great example. Cronometer might say you ingesting 100% of the RDA, but if you are just taking a supplement once a day you are not absorbing 100%. Fortunately, large doses of B12 do no harm. (BTW, vegans HAVE to supplement B12 ). Iron absorption also varies from person to person. Unfortunately, large doses can harm you. excess iron is shed in our poop. If your poops turn black (and rock hard) you are getting TOO much iron. However, that is only likely if you are taking iron supplements. and if that happens it's easy enough to change your daily dose. Also iron is pretty easy to test right at home if that is an issue.(there is a kit you can buy on Amazon. ) It's really hard to ingest too much calcium (but it can be done and can be dangerous). Calcium is a very bulky mineral so you would have to make a concerted effort with supplements to make you sick.
One thing that some dieticians do is make you a meal plan. but really you don't have to pay someone to do that. there are lots of really good meal plans that you can download on the internet. PCRM has a good one. The other good thing about following a meal plan is that it takes a lot of guesswork out of nutrition. And at the end of three or four weeks, you should have a really good idea of what you need to eat in a day. you can even find different kinds of vegan meal plans. Some are WFPB, some are weight loss, some are for athletes. There are even websites that can generate somewhat custom Meal plans. EatThisMuch is pretty good. SparkPeople is good but not 100% vegan (and it spits out a shopping list).
Once you are off the meal plan you can get Dr. Gregars Daily Dozen Checklist. Its an app but i just use a laminated card stuck to my frig. Personally I find it really hard to check most of the boxes most of the time. but it does give you a goal to try to meet.