the purpose is tax savings.
That's probably not realistic. Unless you live in a tax haven, you can't legally save on tax by having an offshore company. If you live in a developing country with limited tax law enforcement, you might be able to illegally not pay tax where you live.
The concepts of tax residence, CFC, and related topics have been covered before on this forum and you can find a lot of information about it if you search.
when you say bad reputation and banking is difficult, you mean we might face problems in receiving payments from our clients? please clarify.
You will have problems opening an account to begin with. It's not impossible, especially if you are OK with an E-Money Institution (EMI) and not a traditional bank.
This is fine if all you need it SEPA/EUR access but for other currencies and non-SEPA payments, the EMI is reliant on correspondents/partners and you may find it difficult to access GBP, USD, CAD, SGD, and so on with an offshore company.
You may also run into problems receiving payments, if your clients' finance departments don't like seeing invoices from tax havens. Some companies will refuse to work with offshore companies.