Read up on your trademark, IP and copyright law. The use of similar marks is not permitted when there is potential for confusion, such as two different software projects, esp with overlapping audiences.
NB: TinkerPop is NOT a "graph database", it is a collection of software libraries for connecting to, using, and managing graph databases and distributed processing platforms. Gremlin is a primary part of that stack -- Gremlin proper is the programming language, and the Gremlin GTM is the runtime.
And for a company name, you decide to use the name of an established programming language and registered mark of a top-level Apache project [2], which has been in use since its inception over a decade ago, and incidentally it's a project and programming language that both your previous employers know well [3].
That's some inspired work, overflowing with creative originality. And to top if off, you have animated graphs floating in the background. Yeah, no possibility for confusion there. There's a name for that you know? Google it and see if you can find the word -- its definition has to do with siphoning goodwill. Who advised you on this and agreed these were wise choices and that this would be a good way to begin?
[1] https://www.underconsideration.com/brandnew/archives/new_log...
When a new third-party project site goes online, SOP is to review the new site/code, understand what it is and how it fits into the overall ecosystem, and then put their project lead in touch with TinkerPop's resident artist and illustrator, Ketrina Yim [2], who is available to create custom artwork/logos and Gremlin character illustrations tailored around the new project's theme.
However, when I dug into this site's docs to see how it was related, I couldn't find a clear connection. And when I checked with our team, they said Apache Legal has been aware of the issue since last year.
[1] Branding https://tinkerpop.apache.org/policy.html
[2] Ketrina Yim, Illustrator https://tinkerpop.apache.org/index.html#committers
Only trademarks registered with various legal jurisdictions are enforceable, such as the "Apache TinkerPop Gremlin" name you registered. Unregistered marks used by an Apache project are simply claims on the mark, which in many cases are not enforceable. One example is the Apache Groovy project, where its PMC members erroneously claim the exclusive use of "Groovy" for their programming language, when in fact their only valid claim is to "Apache Groovy" (and its previous monikers "org.codehaus.groovy" and "Codehaus Groovy").