The profile URL is what turns a name into one person
A name and an employer describe a person. They do not identify one. Large companies have several people with the same name, employers get spelled three ways in one sheet, and every lookup you run on a row like that inherits the doubt. A LinkedIn profile URL ends it. It points at one person, and it is the key that email, mobile and work-history lookups all match best on.
That makes this worth doing as its own job, before you buy any contact data. It also sets the rule. A wrong URL is worse than a missing one, because everything you look up afterwards belongs to somebody else and nothing on the sheet tells you. So a URL is filled in only when one person clearly matches. When two could, you get both, and the agent does not choose.
There is no single chain for this. The agent picks the lookup by what the row holds. An email goes to a provider that resolves an address to a profile. A name and an employer go to a person lookup. What is left goes to a web search of public profiles: quoted name, employer and role.
What you get back
Your list with a profile URL column and a match column beside it: matched on email, matched on name and employer, found by web search, weak match, ambiguous, or not found. Ambiguous rows list the profiles that could be the person, with what the result says about each, so settling one takes a single look.
Nothing is written to your CRM and nobody is contacted.
Variations worth knowing
Keep the work history. The name and employer lookup returns dated work history in the same answer. Say up front if you want it kept. Asking later is a second charge for the same person.
Records in your CRM. Clean and refresh your database runs this on a segment of your own records, pairs up duplicates and writes back what you approve.
Then get the contact details. With URLs on the rows, get emails and mobiles for a list you already have has the strongest identifier it can be given.
Where this goes wrong
Common names. A common name at a large employer, with no title or city on the row, often comes back ambiguous. Add the column that tells them apart, or accept the empty cells.
An employer they have left. The match looks for the person at the company on your row. If they moved on, the lookup may find nobody, or find them shown at a different employer. That is reported as a weak match for you to confirm, not filled in.
Trusting a search hit. A web search result is a lead. It is accepted only when the name, employer and role on the result agree with the row, and it is marked so you can check those rows first.