They want to pay me in company shares worth 100k (as it is stated in our contract).
What does this mean? Does the contract state a number of shares, or an amount? If an amount, who decides the value of the shares, and thus how many shares you get?
Note that there may be several classes of shares (with different rights), which may not all have the same value.
Note that for a private limited company (which is necessarily unlisted), the value of the shares can be quite difficult to find out, as there are many different methods which can lead to very different results.
Some investors may have paid a lot of money for shares because they think that the company will be making a lot of money and/or be sold for a very high amount in 5 or 10 years (which could be used as a current value of the shares), would you want to wait that long? Could you find someone else who is convinced of that valuation to sell the shares to?
Also note that the value can change dramatically depending on the company circumstances (trading not going as planned, or even bankruptcy) and any increase/decrease in the number of shares (you could be diluted to nothing), and that in the case of a private limited company, selling shares is not straightforward (it's not listed on an exchange, so you need to find a buyer and negotiate a price with them).
Of course, it's quite evident that you are most likely going to have a very small share of the company, so even if you have voting rights, they would amount to nothing.
You say that you own yourself a private limited company. Think about it, how much is a share of your company worth? How many shares to reach £100K? Can you easily sell shares of your company? Who to? At what price? How quickly? Would a supplier of yours accept shares of your company as payment?
Should I get shares on my name or under my company, what would be the difference.
Since you seem to be the sole owner and employee of your company this seems to make little difference, but if the contract was with the company, then it's the company who should be receiving the shares, not you, exactly like it's your company who should be receiving any payment, not you directly. Then the company is taxed on that income, and after that you can pay yourself (via dividends or wages), and pay taxes on that income you get from the company.