Racing Point Force India will retain the Formula 1 prize money accrued by the original team after its rivals all agreed.
It is understood McLaren and Williams were among the last to agree to the decision, which required unanimous support.
The biggest concession the new team has made is giving up the points the previous Force India had earned in 2018.
It had been sixth in the constructors' standings, but will now have to start afresh - which will have a bearing on future income.
"The remaining nine teams have signed a document that enables us to keep the money that Sahara Force India earned in years past," said team principal Otmar Szafnauer.
"The biggest consequence is that we start from zero points, we forego the  points because they belong to Sahara Force India, which is not an entrant anymore.
"We will do the best we can and try to score as many points as we can in the remaining races, and see where we end up at the end of the season. And that will determine some of the prize fund for the following year."
Szafnauer thanked rival teams and other F1 stakeholders for agreeing to the change of entry.
"It started off as a share sale that then transferred into an asset sale, for reasons that I don't quite understand," he said.
"Once that happened we needed a new entry into F1, and to gain a new entry in a short period of time takes a lot of work.
"Fortunately with the support of the FIA, FOM, and our fellow competitors, our colleagues within the community, we got it done. I've got to thank the teams for supporting us."
Szafnauer confirmed the Racing Point name is a stop-gap solution.
"The reason is we started the year with Force India as our chassis name. And F1 and the FIA, they don't like chassis name changes, and I understand why, because it confuses the fans," he said,
"We thought it was prudent to keep Force India for the fans.
"The car is still pink, we still have the same sponsors, we still have the same drivers, we have the same motorhome, we have the same employees. If you look at us, we're exactly the same.
"It would have been confusing to remove Force India. Racing Point was added in front of Force India instead of Sahara. That was just so we could distinguish between the old and the new.
"Racing Point just happens to be the name of the company in the UK that own the assets. That's the only reason for the name being there."
Regarding the team's 2019 name, Szafnauer said "we've got to come up with a name that will be lasting, and appropriate, and also approved by the F1 Commission".
He did not deny the obvious suggestion that Lance Stroll, whose father Lawrence led the consortium that saved Force India, will switch to the team from Williams before the end of 2018.
"It is not impossible to change, that's for sure, but a lot of agreements would have to happen," said Szafnauer.
Stroll's current team boss Claire Williams also hinted a change was possible.
"There are a lots of twists and turns in F1, aren't there?" she said. "We've seen that over the past few weeks alone. We'll have to wait and see what the future brings.
"It might be odd if Lawrence owns one team with his son in another, but hey, this is F1.
"At the moment, Lance is contracted to us, he is driving for us this weekend, and as soon as we have more information then we will share that."